The general rule is that one spouse is not typically responsible for the debts of their deceased spouse. The exceptions to this are if the spouses lived in a community property state (you do not) or the surviving spouse has agreed to be held responsible for the debts (e.g. as a co-signer but you did not indicate that to be the case). However, there exists something in the law known as the "Doctrine of Necessities". In some states, debts incurred for medical treatment are considered "necessities" (i.e. necessary expenses of the household). Accordingly, a surviving spouse may be held liable for their deceased spouse's medical bills. While this was once the law in PA my research suggests that it no longer the case. What the surviving spouse should do now is to consult with a local probate attorney to confirm their specific rights/responsibilities.
Note: The deceased spouse's estate is liable for such bills. Consequently, the surviving spouse may still be indirectly affected financially.
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