I know a couple people with businesses like this. In each case, it's because they stumbled into a business that was unexpectedly profitable, but which wasn't something that they really wanted to be in. Usually it's not something that can really be sold either - typically they're taking advantage of temporary market niches, are too small to be of strategic value to a big player, and have a geographically-distributed and lightly-attached employee base that's not a good candidate for a talent acquisition.
Under these circumstances, usually the most rational course is to treat the business like an annuity: while it lasts, milk the profits, do all the stuff you really want to do like travel the world or write a book, and save up a bunch of money. The gravy train will end eventually, but they never wanted to be in this business in the first place, so "losing the company altogether" is a plus.
Under these circumstances, usually the most rational course is to treat the business like an annuity: while it lasts, milk the profits, do all the stuff you really want to do like travel the world or write a book, and save up a bunch of money. The gravy train will end eventually, but they never wanted to be in this business in the first place, so "losing the company altogether" is a plus.