Hi Emma,
When we have residents pass away, the charity will take on the burden of any rent payments from the date of death to the new tenant moving in.
We have never had a resident move into a care home, but I would imagine that once the resident has moved out, the council will have to start paying care home fees in place of the rent as the resident is no longer residing at the property.
Talking to the local council in charge of the residents care would be the first place to look to be reimbursed. The council may be the people you need to get in touch with regards to the rent debts.
Thanks,