Not had it happen, but known it happen. If you've not got a spare set of strings, capo the neck (even better, capo the neck twice, once near the nut and once near the body) to stop the strings wandering, back the string tension right off, then unscrew the trem from the body. See if it'll screw back in, if not get on eBay and buy a Squier one someone's (needlessly*) upgraded on their Classic Vibe. Or buy a replacement collet and arm from Staytrem.
* Didn't stop me doing it, mind, despite Stewart telling me there was no point.