That just happened to me. All the tips on my right hand just peeled off, some of them with a little help. (And yeah, it did look at little bit like that scene in the The Fly.) However none of the ones on my left hand did and I can't use the paper thin nails left on my right hand to pry them off.
This means I have to go about two more hours with one hand looking seriously gnarly and try not to break any of what's left of those nails until I can get out of here and up to Kathy's for a new full set. The reason to be careful of the existing nails is that if there's enough there, I might be able to get the silk wraps laid over my actual nails instead of an acryllic tip. This will save a lot of time in the process.
I was going to pick up laundry on my way home, but hey, priorities.