Professional athletes often stay rich the same way regardless of their sport (MLB, NBA, NFL, etc)
Investing their money wisely and they also get pension checks. A lot of side ventures such as businesses they own or investing and endorsements they've done and do past their professional career. Many also do public speaking.
Some work as sports casters and do other careers after they retire. Look at Michael Strayhan and Alex Rodriquez as examples. Both are retired from their respective sport. Alex works for Fox sports as an analyst/commentator, plus he gets a pension from the MLB. Michael Strahan is a television host with both abc and cbs, game show host, has a men's fashion line, he's done appearances on tv shows and movies.
Not MLB but I work with a guy who is retired from the NBA. While he was in the NBA he finished his education to be a teacher and he's a teacher and a high school coach now. He has plenty of money, he does this because he wants to. He teaches science.
A lady I bowl with her son is retired from the NFL. He invested his money very well, has some side businesses and does a lot of speaking engagements. He also gives back to the community, the school district I work for.. he pays for lunch for all the kids and also pays all the kids' sports fees.