The simplest way to understand your situation is to say that as long as either one of the co-tenants occupy the rental unit that you rented to both of them originally, the original tenancy obligations might continue indefinitely. All three of you will have to agree to either end the tenancy completely, or to let one of the co-tenants out of the lease. They each have a joint a several responsibility to pay the rent, even if the other moves out or dies. If the wife agrees to let the husband be removed from his responsibility to the lease, it will not happen unless you also agree to the change. If you do agree (in writing), then the wife will have to pay the full rent herself, and will probably be forced to find a roommate to help her do so. If the wife fails to pay the full rent in the current scenario (and the husband fails to bail her out by paying), you would serve an N4 Notice to Terminate for Non-payment of Rent in both names, and file an L1 eviction application if needed. If a roommate does move in, however, the wife does not need your permission for this if the roommate is going to only pay rent to the wife. If the wife wants the roommate to be added to the lease as a co-tenant, you would screen that person the same way you would for any new applicant.