Selling a business is a big deal and you should really not do so without getting some guidance from a lawyer. You may not need to hire counsel to handle it all for you, but at least get some good advise first.
That said, usually in the small closely held realm, you would be doing this in the form of an asset purchase as opposed to selling the actual LLC membership interest, but either is possible. This limits the exposure to your buyer regards to underlying LLC liability. But it certainly does not remove it entirely as the assets of the LLC may too be encumbered in some way.
As the Seller, you may still shoulder some liability as well and need to consider the full bundle of issues. For example, any extant contracts or agreements, any outstanding tax liabilities, any personal guarantees, among others.
I will link you to an outline of general business sale considerations to give you an idea of what we look for and I suggest you reach out to a few business lawyers and get some insights. Most of us here, including myself, offer a free phone consult.
The law firm of Natoli-Lapin, LLC (Home of Lantern Legal Services) offers our flat-rate legal services in the areas of business law and intellectual property to entrepreneurs, small-to-medium size businesses, independent inventors and artists across the nation and abroad. 866-871-8655 Support@LanternLegal.com DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed on the basis of this posting.
Whether you'll be liable for any future liabilities will be determined by your agreement with the purchaser. There are a number of considerations when selling a business (taxes, existing contracts, etc.). An asset sale is one way to perform the transfer, but it is by no means the only way or the most advantageous. Consult with a business attorney, there are a number of us in your area.
The answer provided is for general information purposes and cannot be relied upon. In order to provide legal advice, one must engage with a live attorney; this answer does not create such attorney-client relationship.