Normally debts don't get inherited without consent.

This, is more about shifting this debt to the kids or kicking them out of the facility. Further, they are not going to get 'better' the facility's are focused on keeping patents alive to extract as much money from the family as possible not because the elderly actually want to suffer as long as possible or necessarily benefit from the care.

PS: Funeral homes are also setup to prey on people suffering a loss. It's a sick business.