Lateral move

Hi folks, I was wondering : how likely would your current PE firm know you are trying to get a role at another fund ? Given it is a small world, I would have assumed the likelihood of being spotted before even getting an offer quite high, especially if senior people worked at other funds previously. Also, is there a high chance that in last rounds fund B calls your current fund to know about your performance ? In which case, if you do not have an offer from fund B, you are pretty much screwed ? Appreciate any insight on this, and the best approach when you have opportunities elsewhere you want to try out.