Understanding NFA (nondeterministic finite automaton) with a null transition
If a run of an automaton reaches a state where it has no legal transitions for the next input character, that run rejects immediately.

So, in your example, if the automaton makes the null transition, it can read $bb$ while staying in state&nbsp;$2$.  But when it reads the&nbsp;$a$, it has no legal transition so that run rejects.  Any run that stays in states $0$ and&nbsp;$1$ must also reject, because those two states are rejecting states. Therefore, the automaton does indeed reject all strings containing $bba$.