Inherited tenant woes

[Michael R.]

Hello,

I inherited some tenants when I purchased my house hack duplex last June.  The mother was in the hospital, father had a stroke and was receiving homecare, and their son (24 yrs old) was working part time.  They've been good about paying on time and have only been a few days late in the past (there is no late fee in their lease).  Unfortunately the mother passed and I've been doing my best to remain delicate yet business-like with my property management since I really feel bad for the family's misfortunes.  

Just recently the father moved out to a long term care facility leaving the son behind.  They were on a two year lease which ends at the end of April and the only two names that are on the lease are the parents who have essentially broken their lease agreement.  I received a call from the son on the 29th of last month informing me that he will be a week late with the rent, maybe more, and was wondering if he could make a partial payment.  I told him my policy is to only accept payments in full.  I don't want to hit him with an eviction notice since I know he's actively trying to come up with the money, but I also don't want to get burned.  The other concern I have is that, once the lease is up, this young man won't have enough to pay security deposit and first months rent on a new place and I might be stuck with him.  What would you do in this situation?

Thank you,

Michael