Nyc - Two Tenants On A Lease Expired, Can One Tenant Just Move Out And Relinquish All Responsibilities?

We rented to a couple last year, we signed a lease with both of their names. The lease expired in August and went into month-to-month. They broke up and the male tenant wants to leave. He gave his 30 day notice end of December. We handed the woman notice to vacate mid December giving them 60 days (till end of Feb) to move. The male tenant also tells us to use the sec deposit to cover January.

Is the male tenant still responsible for the woman's tenancy or can he relinquish all responsibilities once he has left?

Our worry is that the male tenant has solely paid for all rent up till now and we are not even sure if the woman can pay rent at all. The male tenant also closed his utility accounts and the woman has not reopened them. We just want them both out together at this point and move on but worry she won't leave willingly and the man is no longer in the picture.