It happened to me yesterday while trying to add more RAM to my recently acquired Portégé. Annoyingly, as is the trend with ultrabooks, the RAM is only accessible by removing the entire back of the laptop, as opposed to unscrewing a memory panel. Anyway, I get to the last screw - it must have been a bit tight - and lo and behold, the Phillips cross becomes more of a star.
After being frustrated for long enough that night, I screwed all the other screws back in and left it for the night (in the process, the second-last screw got stripped as well). This morning I went to Bunnings to get a screw extractor. It seemed quite a handy tool. Of course, it didn't work.
However, after reading about numerous methods of how to resolve screw problems, I sort of did my own thing.