Lease is ending and one tenant wants to stay after a break up

[Rachael Perez]

Lease is ending and one tenant wants to stay after a break up between them. This was a couple who had -over text -told me they wanted to renew their lease which expires in 2 days. They hadn't sent in the signed copy and I told them I would need it with the new rent on the 1st. 
Today the man called me to tell me that she had moved in with her parents and he wanted to maintain the rental on a month-to-month.
My question is what do I do about the security deposit and the last months rent that they paid together?  
ie, Do I need to Distribute the funds to them both and then recollect them in only his name?   Also since the rent has gone up I'm assuming the last months rent and security deposit )1 no rent) should go up commensurate right?