These comments are made for educational purposes only and do not constitute legal advice. No attorney-client relationship exists between us.
While understand the desire to clear up your mother's reputation, there is no reason to do it. Her estate will have pay for her funeral and remaining medical bills. Only then, if there is anything left, will the credit cards be able to collect. If there is nothing left in the estate, too bad for the creditors. Additionally, if there has been no payment on the cards for 4 years or more, the creditors can't sue to collect anyway. No relatives will be responsible for the unpaid debt. There's no reason to mention your sister to anyone.
You have asked similar questions with slightly different scenarios so I hope what you gleen from all of us trying to help you makes sense.
Assuming the statute has run (and that it is the Texas statute - problem is - as I have told you before - when you enter a contract the contract can control where the case would original from. For example, my contract says that the place is Houston. But, the cards could list another state with a different statute of limitations.)
If the debts are time-barred, there is no requirement to pay. Tell the debtors to quit harassing, that there is no estate (if there is not or it is too small), and to leave you alone.
Be aware that if your sister knew that the debts would not be paid or incurred them after your mother's death, it could be a different situation.
I recommend that you look at the website of the credit cards in question to see if it names a different place than Texas for lawsuits & disputes, and if so, research that State's statute of limitations.
You might also want to use a lawyer to write letters telling the company (ies) to quit harassing you because your mother is deceased & there is no estate (if that is correct.)
This statement is for educational purposes. We have no attorney-client relationship. My answers are guesses based on your claims.