why is the NL solution PATH negated unsufficient to prove unreachability I'm currently reading into complexity classes and one think will not fit into my head.
We are investigating NLogSpace with the Path/reachability problem.
There is a nondeterministic LogSpace algorithm which can solve reachability, but its inversion does not prove nonreachability because "it could miss a path". How is it possible to miss a path? Wouldn't it imply that the reachability test might doesn't work? 
Can somebody please explain it to me? Thank you.
maybe i was a bit to specific, i had a general misunderstanding in how non-deterministic machines work. Here is what i figured:

an accepting nondeterministic turing machine always gives the right answer ("found something, therefore a solution exists",
on the other hand, a reject means "did not find anything" which is not the same as "there is no solution"

therefore a reject can't be trusted and any algorithm which uses a reject from a non deterministic (Existance) machine has to double check. Also this implies, that a non-deterministic machine could give a false negative.