As a landlord: If the income was sufficient to pay the rent, and all parties agreed to this and signed a contract, and then payments fell behind only because they were forgotten and for no other reason, then the money to catch up on the rent should be there and used as such immediately. The landlord can’t forget to pay the mortgage. The bank has investor money that was lent out and needs to be returned. There’s no free magical money here. Everyone owes and payments need to be made. Alzheimer’s may be the reason for missed payments, but it doesn't mean it can't now be paid once its remembered.
Your suggested solution is certainly not from a landlord. It’s from tenants that want their cake and to eat it too... a free ride on $15k owed.
The eviction on your record is the last thing you should be worried about. DO the right thing.
This problem is entirely of the tenants making and entirely in the tenants hands to resolve. As a landlord, I can work with tenants. I have compassion for those sick and I would work with a situation like this to create a workable repayment sturcture. I certainly wouldn't let it get anywhere near this far behind though. If the tenants are not interested in the effort it will take to resolve this, then that's a reflection on them. It also reflects poorly on the landlord's business skills to allow this to get this bad.
An eviction should absolutely be on the record of all adults who lived there. Everyone living there benefited from the $15k in free cash.