Echoing the question asked by Mr. Devoss, was this an asset purchase or an LLC interest purchase? If it was an asset purchase, the LLC would still be owned by your mother. She may want to "dissolve" the LLC which involves filing dissolution documents with the State of Maryland (if the LLC is a Maryland LLC). She would also file a final personal property tax return with the State and likely a final income tax return with the taxing authorities. She may be required to terminate certain licenses or permits. If the sale was a sale of all of her ownership interest in the LLC, the purchasers will likley keep the LLC in existence and be responsible for filing property and incime tax returns.
Did you parents sell their membership interests in the LLC or was it an asset transfer only? The purchaser of the LLC will be responsible for the filing of a tax return if the purchase was a membership transfer. The purchasers will file an appropriate tax return.
I agree with my colleagues that the reporting requirements depend on the exact structure of the sale. I suggest they consult with a local business attorney to review all facts and advise accordingly. The IRS will know of the sale because your parents will report it on their tax return. If needed, they can also file a change of address form. If they sold the LLC, check with the state's corporation division if an amendment has been filed.
The above "answer" is for discussion purposes only and is neither intended as legal advice nor to create an attorney-client relationship. An attorney-client relationship is not created until after an in person consultation and I agree in writing to provide representation. I am licensed solely in the state of Arizona. You should consult with a knowledgeable attorney in your jurisdiction.