It is important to remember that a patent does not give anybody the right to do what the patent covers. For example, if I had a patent on a more effective delivery system for MDMA or LSD, having a patent doesn't change the fact that those drugs are considered Schedule 1 and illegal under almost every circumstance -- meaning that my delivery system couldn't be used even though I had a patent on it.
While a patent doesn't give the patentee the right to practice the invention, it does give them the right to sue people to stop them from using the invention (or to recover financial damages). The expiration of a patent simply means that the owner of that patent can no longer sue anybody for using the inventions claimed in the patent.
Those things together mean that the concept of "public domain" for a patent is quite limited. Taking the game "monopoly" as an example, the game was initially covered by a patent, by copyright, and by trademark law (though it does seem likely that recent Supreme Court decisions may have rendered that game not patentable today). When the patent expired, the copyright and trademark in the game remained in place. So while a company could sell a game with the same game-play mechanics that were claimed in the patent without fear of being sued for infringing the patent, that company could still be sued if they violate the copyright to the game or call it "Monopoly", despite the trademark.
The bottom line is that the expiration of a patent simply means that the patent is no longer in play (subject to the revival issues discussed in other answers). However, there are other intellectual property rights (copyright, trade secret, trademark, trade dress, state-level trademarks, rights of publicity, etc.) that can give rise to significant liability. The expiration of the patent will not impact those other rights. The mere expiration of a patent does not mean that anybody can freely practice everything in the patent until they are satisfied (preferably by a lawyer's opinion letter) that what they intend to do is (a) legal, and (b) does not violate any other IP rights.
The other thing about patents is that it is common for a single patent application to result in numerous patents. There is even a thing called a "terminal disclaimer" that is used when a second patent claims something not significant different than the first patent. Because patent maintenance fees are expensive, infrequently a patent owner will allow one patent to go expired for non-payment of fees, counting on other patents in the family to cover the same material. You'll want to go to https://portal.uspto.gov/pair/PublicPair and look up the expired patent. First, make sure it is really expired. Second, check the "continuity" tab and see if there are other patents still in force (or pending applications) in that patent family.
Perhaps most importantly, you need to seek proper legal advice. A good IP lawyer should be able to walk you through it. It is tough to answer this in the abstract, and the facts specific to what you want to do will be critical in having a lawyer give you the right answer.
