If I were to use a vibrating toothbrush to masturbate with and the end came off in my vagina would it eventually fall out?

Maybe... Any foreign object inserted into the vagina could "fall out" on its own. Using your fingers, try to see if you can remove it. If not, a doctor can remove it during a simple pelvic exam in the office or local Urgent Care. Better to see about this sooner than later.