A Bankruptcy does not automatically disqualify a borrower from receiving an FHA loan. If your bankrupcy was discharged 2 years ago you may be eligible today for an FHA loan program. If you bankruptcy was discharged less than two years ago and you have extenuating circumstances you might still be eligible to qualify.  You can find out more by applying here!.   Same rule applies for borrower with chapter 13 bankruptcy.
A chapter 13 has some different requirements as a chapter 13 bankruptcy may still qualify if the  lender is willing to do a manual underwriting and the borrower has a satisfactory history of payments under their Ch 13 pla.