Yes, you are responsible for the rent--and you would have been responsible even if the sublessee had signed the agreement. That is because on a sublease, as opposed to an assignment of a lease, the sublessee does NOT take over your lease and you are not released from the lease; rather, the sublessee leases (subleases) from you, and you are the sublessee's landlord while remaining the main landlord's tenant. You are still obligated to the landlord as per the terms of your lease; so you pay the landlord, while the sublessee pays you. (That's from a legal point of view; as a practical matter, it could be arranged that the sublessee's payments go directly to the landlord, bypassing you, but legally it is that you still owe the landlord and the sublessee owes you.)You would have a claim against the sublessee for the rent for the time he or she was there, if it has not already been paid; and likely for another 30 days of rent at least, since even with no in-force written lease, a tenant or subtenant must give 30 days notice terminating his or her tenancy. You could potentially sue the sublessee for these amounts.If you are not actually inquiring about a sublease situation, where you remained on the lease and the subtenant leased from you, you should re-post your question with additional detail.