Happens on a regular basis.
The Poughkeepsie NY airport is in close proximity to the White Plains airport (and has its runway in the same orientation), and there have been instances of jumbo jets getting confused about which airport they were looking at and landing at POK by mistake. Unfortunately, Poughkeepsie's runway is not long enough for them to take off again unless they are thoroughly stripped down -- meaning unbolt optional accessories like passenger seats.
So, yeah, there are usually ways to get the plane unstuck. They just get more expensive as the runway gets shorter.