It is known that when NFA's accepting states are swapped with rejecting states, the recognized language is not complement of the original language. For some language, it may be the case that some strings that were recognized in the original NFA may still be recognized in the state-swapped NFA. My question is, is there a language $L$ that in the original NFA a string is not recognized(rejected), but in the NFA where accepting states become rejecting states and rejecting states become accepting states the string is also rejected? 
When states that are not accepting states become accepting states in NFA, what happens?
automata;finite automata