<PAGE>   1
                  EXTENSION OF CONVEYANCE AND INDEMNIFICATION AGREEMENT

         This EXTENSION OF THE CONVEYANCE AND INDEMNIFICATION AGREEMENT dated
October 1996 (the "Extension Agreement") is entered into between the FEDERAL
DEPOSIT INSURANCE CORPORATION ("FDIC") in its corporate capacity ("FDIC
Corporate"); the FDIC Receivers (as defined in that certain Settlement Agreement
dated as of June 22, 1994) (whether one or more, the "Indemnitee"); FCLT Loans,
L.P., as an assignee of First City Bancorporation of Texas, Inc. ("FCBOT") and
its related entities ("FCBOT Affiliated Entities") (FCBOT and the FCBOT
Affiliated Entities are collectively referred to as the "First City Parties")
and FIRSTCITY LIQUIDATING TRUST ("FCLT"). Capitalized terms used in this
Agreement and not otherwise defined shall be given the same meaning as set forth
in the Settlement Agreement (as defined below).

                                   RECITALS:

         WHEREAS, pursuant to the terms of that certain Settlement Agreement
dated as of June 22, 1994, between FDIC Corporate, the FDIC Receivers, and the
First City Parties, as amended as of January 30, 1995 (as amended, the
"Settlement Agreement"), the FDIC Receivers agreed to, among other things, (i)
effect distributions of the Surplus (as defined in the Settlement Agreement)
generated out of the First City Bank Receiverships (as hereinafter defined) to
the First City Parties and (ii) defend certain litigation and other disputed
matters of the First City Parties, the FDIC Receivers, FDIC Corporate and/or
certain other parties: and

         WHEREAS, FCLT Loans, L.P. is an assignee of the First City Parties; and

         WHEREAS, FCLT is the sole limited partner of FCLT Loans, L.P.; and

         WHEREAS, the parties find it to be mutually desirable to terminate the
"Cash Holdback Reserve" established by the Conveyance and Indemnification
Agreement dated October 1996 prior to the anticipated termination date; and

         WHEREAS, the FDIC desires to make an early final payment in the amount
of $2,514,550.28(1) (the "Final Payment "), and

         WHEREAS, as a condition to making the Final Payment by the FDIC prior
to the scheduled termination date and as consideration therefor, the parties
desire to enter into this agreement whereby FCLT Loans, L.P. will continue to
provide indemnity to the FDIC against any known or unknown liabilities, claims
or expenses in an aggregate amount up to $10 million, associated with the First
City Bank Receiverships.

----------
(1)   As of 1/31/99


<PAGE>   2


         NOW THEREFORE, in consideration of the mutual promises and covenants
contained in this Extension Agreement and other good and valuable consideration,
the receipt and sufficiency of which is acknowledged, the parties agree as
follows:

          1.   DISTRIBUTION OF HOLDBACK ASSIGNMENT OF RIGHTS

               a. ASSIGNMENT OF CASH HOLDBACK. As the final cash payment
          pursuant to Section 5.1 of the Settlement Agreement and the terms of
          the Conveyance and Indemnification Agreement dated October, 1996, the
          FDIC Receivers hereby transfers, assigns and conveys unto FCLT Loans,
          L.P. all of FDIC Receivers' rights, title and interest in and to the
          Cash Holdback.

               b. INDEMNIFICATION. As a condition to and in consideration of the
          assignment of the Cash Holdback from the FDIC Receivers to FCLT Loans,
          L.P., FCLT Loans, L.P. agrees to extend its indemnification of the
          FDIC and agrees to indemnify the FDIC against any known or unknown
          liabilities, obligations or expenses incurred by the FDIC which may
          arise now or in the future until the Termination Date (as hereinafter
          defined) associated with the FDIC Receivers (the "Indemnified
          Obligations"). Such indemnification shall be subject to the conditions
          and limitations, and governed by the procedures, set forth in Section
          2 hereof.

          2.   INDEMNIFICATION

               FCLT Loans, L.P. shall indemnify, and reimburse FDIC for all
          liabilities, obligations, expenses, costs and any loss incurred by the
          FDIC associated with the FDIC Receiverships, including, but not
          limited to, expenses incurred in connection with the Outstanding
          Claims; provided, however, that in no event shall FCLT Loans, L.P.'s
          liability under Section 1(b) and this Section 2 exceed ten million
          dollars ($10,000,000). The term "expenses" as used herein shall
          include, but is not limited to, all research costs, accounting
          charges, review fees, attorneys' fees, court costs, transcript costs,
          fees of experts, witness fees, travel expenses, duplicating costs,
          printing and binding costs, telephone charges, postage, delivery
          service fees, and all other disbursements or expenses of any kind
          incurred in connection with or related to the FDIC Receivers and in
          defending litigation, preparing to defend, investigating, or being or
          preparing to be a witness in litigation.

          3.   GENERAL

               a. DURATION OF AGREEMENT. This Extension Agreement shall continue
          until and terminate on Midnight C.S.T., January 3, 2000, or the final
          termination of FCLT (whichever date is later, the "Termination Date"),
          unless otherwise extended by the parties.



<PAGE>   3

               b. SEVERABILITY. If any provision or provisions of this Extension
          Agreement shall be held to be invalid, illegal or unenforceable for
          any reason whatsoever; (i) the validity, legality and enforceability
          of the remaining provisions of this Extension Agreement (including,
          without limitation, each portion of any section of this Extension
          Agreement containing any such provision held to be invalid, illegal or
          unenforceable, that is not itself invalid, illegal or unenforceable)
          shall not in any way be effected or impaired thereby; and (ii) to the
          fullest extent possible, the provisions of this Extension Agreement
          (including, without limitation, each portion of any section of this
          Extension Agreement containing any such provision held to be invalid,
          illegal or unenforceable, that is not itself invalid, illegal or
          unenforceable) shall be construed so as to give effect to the intent
          manifested thereby.

               c. IDENTICAL COUNTERPARTS. This Extension Agreement may be
          executed in one or more counterparts, each of which shall for all
          purposes be deemed to be an original but all of which together shall
          constitute one and the same agreement. Only one such counterpart
          signed by the party against whom enforceability is sought needs to be
          produced to evidence the existence of this Extension Agreement.

               d. WAIVER. No delay on the part of the Indemnitee in exercising
          any power or right shall operate as a waiver thereof; nor shall any
          single or partial exercise of any power or right preclude other or
          further exercise thereof or the exercise of any power or right. No
          waiver by the Indemnitee of any right hereunder or of any default by
          FCLT Loans, L.P. shall be binding upon the Indemnitee unless in
          writing, and no failure by the Indemnitee to exercise any right
          hereunder or waiver of any default FCLT Loans, L.P. shall operate as a
          waiver of any other or further exercise of such right or of any
          further default.

               e. HEADINGS. The headings of the paragraphs of this Extension
          Agreements are inserted for convenience only and shall not be deemed
          to constitute part of or to effect the construction of this Extension
          Agreement.

               f. MODIFICATION AND WAIVER. This instrument contains the entire
          agreement of the parties with respect to its subject matter. No
          supplement, modification or amendment of this Extension Agreement
          shall be binding unless executed in writing by all of the parties to
          this Extension Agreement. No waiver of any of the provisions of this
          Extension Agreement shall be deemed or shall constitute a waiver of
          any other provisions (whether or not similar) nor shall such waiver
          constitute a continuing waiver.

               g. PARTIES BOUND. The rights of the Indemnitee hereunder shall
          inure to the benefit of its successors and assigns. The terms of this
          Extension Agreement shall be binding upon heirs, executors,
          administrators, successors, and assigns of the parties hereto. All
          representations, warranties and agreements of FCLT Loans, L.P. shall
          bind FCLT Loans, L.P.'s personal representatives, heirs, successors
          and assigns.


<PAGE>   4


               h. NOTICE. All notices, requests, demands and other
          communications hereunder shall be in writing and shall be deemed to
          have been duly given if (i) delivered by hand and receipted for by the
          party to whom said notice or other communication shall have been
          directed, or (ii) mailed by certified or registered mail with postage
          prepaid, on the third business day after mailing:

                (a)    If to Indemnitee, to:

                Mr. Thomas J. O'Keefe, Assistant Director Field Operations
                1910 Pacific, Suite 1700, Dallas, Texas 75201

                with a copy to:

                Regional Counsel FDIC Legal Division,
                1910 Pacific, Suite 1700, Dallas, Texas

                (b) If to FCLT or FCLT Loans, L.P., to:

                Mr. Robert W. Brown, President, FCLT Loans Asset Corp. 
                First City Tower, 1001 Fannin, Suite 505, Houston, Texas 77002

                with a copy to:

                G. Michael Curran 
                Akin, Gump, Strauss, Hauer & Feld, L.L.P. 
                1700 Pacific Avenue, Suite 4100 
                Dallas, Texas 75201-4675

          or to such other address as may have been furnished to Indemnitee by
          FCLT or FCLT Loans, L.P. or to FCLT or FCLT Loans, L.P. by the
          Indemnitee, as the case may be.

               i. GOVERNING LAW. The parties agree that this Extension Agreement
          shall be governed by, and construed and enforced in accordance with
          the laws of the United States of America, and to the extent such law
          is not applicable, with the laws of the State of Texas.


<PAGE>   5

         IN WITNESS WHEREOF, the parties hereto have executed this Extension
Agreement on the day and year first above written.

                                   FEDERAL DEPOSIT INSURANCE CORPORATION, in its
                                   corporate capacity                           
                                                                                
                                   By:     /s/ THOMAS J. O'KEEFE                
                                           -----------------------------------  
                                   Name:   Thomas J. O'Keefe                    
                                   Title:  Assistant Director Field Operations  
                                                                                
                                                                                
                                   FEDERAL DEPOSIT INSURANCE CORPORATION in its 
                                   capacity as the FDIC Receivers               
                                                                                
                                   By:     /s/ THOMAS J. O'KEEFE                
                                           -----------------------------------  
                                   Name:   Thomas J. O'Keefe                    
                                   Title:  Assistant Director Field Operations  
                                                                                
                                                                                
                                   FIRSTCITY LIQUIDATING TRUST                  
                                                                                
                                       By:    FLEET NATIONAL BANK, as Trustee   
                                                                                
                                   By:     /s/ SUSAN T. KELLER                  
                                           -----------------------------------  
                                   Name:   Susan T. Keller                      
                                   Title:  Vice President                       
                                                                                
                                                                                
                                   FCLT Loans, L.P., a limited partnership      
                                                                                
                                       By:    FCLT LOANS ASSET CORP.,           
                                              its General Partner               
                                                                                
                                   By:     /s/ ROBERT W. BROWN                  
                                           -----------------------------------  
                                   Name:   Robert W. Brown                      
                                   Title:  President