Can a menstrual cup get stuck?

Concerns about your cup getting stuck are really normal. 

The most important thing to remember is your cup cannot get lost! When removing your cup relax and take your time. The more relaxed you are the easier it will be to remove. 
How high your cup sits depends on how high your cervix is, if you have a high cervix your cup may be slightly trickier to remove but go into a deep squat pose, this will encourage your cup to move down by lengthening you pelvic floor, bearing down can contribute to weakening of your pelvic floor, if you need to bear down do so gently as if passing wind.