That’s incredibly awful.
I really hope there are no legal grounds to make the ex-husband pay the back rent.
do you know if this is about "breaking a lease" or unpaid rent? shouldn't the landlord have requested first and last month's rent before the tenant moved in?
If not, I'm guessing the woman's estate would be responsible for the rent if they want to keep the place for a little while before they move her stuff out. And if her estate can't pay it, then whoever else (presumably her ex-husband) wants to keep the apartment. But I can't see how they could go after the ex-husband for back rent if his name is not on the lease.