Am I liable for husbands debts?

This is very fact specific. If you never guaranteed the debt, you may not be. On the other hand, if you used the card and ran up charges and paid for the charges the company may claim, you were a co borrower with privileges and obligations. Another issue is whether or not estate funds (not your funds) are sufficient to pay off the debt. Do not list to creditors who claim you must pay these obligations. Review the debt notices, the credit card contract and if it exists the Last Will and Testament of your husband with an IL probate lawyer. Please read carefully my explanation of unfair debt collection at the bottom of this reply.
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The prior federal administration severely weakened most state’s laws against excessive interest. Unpaid debts now have practically no ceiling on interest which means the final bill can be much more than the original debt.
When you have received a collection notice, lawsuit or even a judgment on an old debt which may have already been paid, or belongs to someone else, or has been discharged in bankruptcy, keep the following in mind. After a creditor writes off your debt, it can then be sold to a collection agency. That agency may sell it again and the next one again. By the time the debt is assigned to a law firm, it can be years pass the statute of limitations, all of the original contracts have been lost and there may be no legal foundation for enforcing the debt. One way of knowing this is that the agency will have no discernible address or they will say they are collecting from a creditor, but the creditor does not know who they are. They will call you at work , and they will not listen to any explanation at all. They will refuse any suggested payment plan and demand a large sum at once. Often these collection agencies and even law firms will file a suit against you, misspell your name, or deliberately send it to the wrong address. You have no notice but they go to court anyway, get a default judgment against you when you do not come to court, and file a judgment lien on your assets such as a home you are trying to sell, or they report you to a credit bureau as a deadbeat. You are allowed to send a 100 word explanation in writing to the three credit bureaus (which they must print) as to why the debt is invalid. Also, many attorneys will take such a case on a contingency basis. A Violations of the fair debt collection act has a fee shifting rule (the creditor pays your attorney). Not only do you get the debt out of your life, you may get a financial award also. Be sure to write to your congress representative to have a stronger federal law to restore a ceiling on interest and to curtail these illegal collection practices.

LEGAL DISCLAIMER
Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Sarno strongly advises the questioner to confer with an attorney in their own state to acquire more information.

If you were a joint card holder the answer is yes. The credit cards may attempt to collect from your husband's estate. Also, be aware that a credit card company might pursue you under the "family expense" doctrine -- ie debt that is incurred for the support of a family member can be attempted to be collected from the spouse or parent of a child.

Please consult an experienced deb/estate attorney in your area.

You are liable for anything he charged on the account that were necessities, such as food, clothing, medical care, or housing.