If she was not married at the time, only the elderly woman (and now that she has passed, her estate--or her money and other assets, like any home, left behind when she died), would be responsible: other adults or family are only responsible financially if they signed paperwork taking responsibility. So the hospital (or rehab center, nursing home, hospice, etc.) can try to get the money from whatever the woman left behind, but they are limited to what she left behind; they cannot sue or otherwise get payment from other family members who never actually agreed to become responsible for any debts or bills.If she was married, her husband would be liable: spouses are liable for the "essential" costs and debts of their spouses, like medical care.