finite state automaton - Is this NFA correctly accepting inputs that end with a 00?

Question

In a lecture it was said that this NFA accepts inputs ending with two zeros or inputs=0: https://ibb.co/9Wt0j7J . The alphabet is {0,1}

But if the input would be 001 we would on some path also end up in the acceptance state (z2) but it would not be possible to go back to another state when reading the last character, the one. That would mean, a wrong input was accepted. So, my question is: Is the NFA really constructed correctly without changing anything? And if yes, why? Can I just assume that we go to an "empty (invisible) state (error state without mentioning it explicitly)" or something like that if there is no other arrow to another state?

Answer 1

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