This really depends on the context in which this occurs. Sometimes it is not obvious, but the game can be over with what looks like an unresolved board position. Deeper reading will usually show whether or not a group that may be in question is alive or not, but if you feel that your opponent is passing and you still have valid moves on the board, go ahead and try what you think you can. If a group does not have two eyes and it can not capture something around it to make the 2 eyes, than your opponent does NOT have to completely remove it from the board. That is what the "remove dead stones" part is for at the end of the game. If they were right to pass, than they will be able to defend what they have claimed is solidly theirs. 
You should not, however, pass before the territories are solidified (walled off). Flyordie doesn't really have any kind of counting system, so it will only give solidified territory in the end, so make sure that all the moves on the first line etc are finished before passing. Hopefully I answered your question. If you are referring to the pass-reject bug that currently exists, I can't really offer any help there. If you see someone doing it, take a screenshot and report the person doing it (though I'm honestly not sure if this is against the rules of conduct or not, so reporting it may something done about it or it might not...)