Yes. But.
There's a catch. If you're imagining a rich person ponying up the dough and declaring themselves leader of the new free world, they better be able to defend it. As a new country, they'll have no protection from anyone, either other sovereign nations or just regular run of the mill bandits or cartels.
They could attempt to be recognized by the UN, or get one of the larger powers to otherwise support them, but some of those nations might just decide to annex them instead seeing as how the rich person doesn't have any anti-aircraft missiles. As a result of this, it would be incredibly foolish for countries to go off and sell their lands willy-nilly, which is one of the reasons you don't see it happen. If the U.S. decided to sell Florida to Elon Musk, he could then make a deal with either Russia or China for them to house military bases there and maybe he could make his money back in the process. Win Win Lose.
If your question is about private purchases of land between private parties, you can't create a new country that simply. If, instead of buying it directly from the Federal Government Elon Musk just bought all of the land in Florida via private transactions, he would still be charged with one of the forms of sedition in U.S. Federal Court if he declared himself Emperor of Floridistan after he was apprehended by Federal Marshals. Unless he also can defend Floridistan from the U.S. (and bandits and cartels), in which case he is Emperor there. But if he could do that I wouldn't think he would go through the trouble of actually purchasing the property to begin with.
Countries can sell their land off to other nations to raise funds also, and they have. It's generally a bit safer than selling it to some individual who may turn out to be an actual crackpot, but your mileage may vary. France sold a large portion of their claims in North America to the United States under what's become known as the Louisiana Purchase in 1803 for a cool $15,000,000. You can see other examples of these types of purchases on Wikipedia.
It used to be more common under Feudal systems for titles of nobility to be bought and sold, often carrying with them rights to land and retainers, but "countries" in that time frame were less well defined under those systems and may at times have spanned what we think of as "counties" today. It often occured more frequently when a given monarch needed some quick cash for some reason or another. King James I in 1611 created a class of 200 Baronets in order to help finance repayment of debts related to the Nine Year's War. I doubt most people would agree in the majority of these cases that it counts as the selling of sovereign land, but rather a sovereign giving someone permission to own it.