Is there a DFA that accepts no string, but has at least one final state?
Consider a 2-state DFA over the alphabet $\{a\}$ (single character alphabet) that accepts only the empty string:



In this DFA, state 0 is the start state, and also the only accepting state. Now, if state 1 were the start state (but state 0 still the only accepting state), what strings would this machine accept?