Is there a DFA that accepts no string, but has at least one final state? Is there a DFA that accepts no string, but has at least one final state?

I think it would be possible to make a DFA that accepts no string only by creating no final states or by making sure that the final states are not accessible. But how can a state not be accessible if a DFA has all of its transitions defined?
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?