No, not everyone matches / post-matches. However, there are plenty of post match positions open, but not necessarily in a location you want to go to. You also have to act quick on Match Day - most places will want to fill post-match spots within 2-3 weeks.
If you don't get into a program, you go work somewhere usually. You don't need a residency to get a dental license in most states! In general though, if you want a spot, you'll be able to find one somewhere, you just have to keep your mind open, and be willing to jet to interviews on a few days notice. The best way to avoid this however, is to apply to enough positions prior to the match - just applying to 3-5 can be a bad idea, especially if they are all competitive programs.