If two people are married but do not share joint credit cards will either spouse inherit the debt if one dies?

If married but do not share joint credit cards will either spouse inherit the debt if one dies.. Also according to my search if they both are entering a care facility with Medicare and Medicaid the credit card debt they have approx 4000k because my aunt is dementia but we could not declare her incompetinant unfortunately in time... they will not have enough to pay the facility and credit card payments.