# Does a PDA immediately accept if at final state with empty stack?

If computation on a PDA reaches a final state with an empty stack, will it immediately accept, regardless of whether or not the input tape has ended. For example if I have a PDA to recognize the language of strings where $a^nb^n$, if it was fed the string "aaabbba", will it stop after seeing the last "b" if the stack were empty and it was in an accept state? Or would the PDA, need to specify a dead state from the final state for incorrect strings?

For example, this PDA would seem to accept "aaabbba":