I am a lawyer, but not a civil lawyer so this advice also comes with the caveat/disclaimer to contact an attorney that specializes in the credit arena for the most accurate information. That said, your hubby is right and there is a statute of limitations on debt collections (5 or 7 years, I think). Companies will sell their uncollectible accounts receivables to companies for pennies on the dollar who in turn hunt you down and try to scare you into paying it. Note: the debt will become active/legally collectable again if you, in writing, agree to pay any amount to the collection agency so watch what you do when dealing with these people-they know the law and how to get the money.
Also, in regards to a lien on your home: there is no way Sears or any other unsecured lender can do that. In order for a lien to be put on your home for a bad debt, the home (or other collateral) must have been negotiated for in the original contract in order to get the credit. The most common examples are a mortgage, a builder’s lien, or any other secured transaction (for more info on secured transactions, see Article 9 or the Uniform Commercial Code) that specifically and unambiguously secures the debt with your home or other collateral.
Bottom line is do not worry- Sears cannot take your house or even secure a debt after-the-fact with a lien on your home unless it was bargained for in the original contract. If the Sears debt was just for a credit card (and not to put up siding/windows, etc.) it will be an unsecured transaction and they have no recourse.
I hope this helps!