About 4 days ago I was in 1st place in my current league and I had 3,8k manager points. In that day I lost my game, dropped to 3rd and in the end of the day had only about 2,9k points. Can I lose points or switch with another player?
Hello and welcome, that's how the manager list and points work. The higher you are on the league standing the more point you get, winning more games against real active managers, wining the league and cup also get you more points.
And vice versa.
So yes, you are likely to drop points when you drop down the league standings.