I know that you can use a cigarette lighter, very briefly, to burn off the stuck-on ink off the ball… otherwise the ball will pop out because the ink behind it turns to steam, I assume.
I believe there’s a chemical (maybe isopropyl alcohol?) That you can apply to the ball to dissolve the ink as well.
Pens can often pick up paper fibers that gum up the works. In the case of ballpoints I can see this being a pretty permanent problem once it builds up enough to stop up the pen
The ink can dry out or some contaminant can get on the ball and preventing it from rolling. What I usually do is run the ball along the sole of my shoe (or use anything that has high friction material) 9 times out of 10 it makes the pen work again.