Isn't that just an AND gate? If input 2 is off then the output is always off, regardless of input 1. If input 2 is on, then the output is only on when input 1 is also on. Therefore, the output is on only when both inputs 1 and 2 are on.
Nevermind, I think I see what you mean. Your wording regarding input 2 being off confused me.
When input 2 is on, the output matches the state of input 1 as you said.
However, at the moment input 2 switches to off, the output freezes in its current state, and maintains that value regardless of changes to input 1. Switching input 2 to on again unfreezes the output and allows it to match input 1 again.