Renter did not sign the lease but confirmed the agreement by email and payment

[Connie Tan]

In May, my renter and I agreed to add a purchase option to the lease so they would have the exclusive right to purchase my house at a set price within a year.  In return, they had to give me $2k+ non-refundable funds.  They emailed me acknowledging receiving the lease and agreed to sign (I have copies of the emails).  They also subsequently deposited the exact amount of funds to my account.  Now, 6 months later, the husband is in jail and the wife realizes that they won't be able to get the loan and she wants to apply the $2K to her rent.  And she told me that she purposely did not send back the signed lease so she could back out from the agreement and get the money back.  The house is located in a summer rental area so the real estate market is practically dead until May/June.

My question: do I have a binding agreement?

Thank you for your help!