Do you mean you "saw" oil in the bilge? I assume the engine wasn't talking to you... or was it?When open engine bay say “oil” in the bildge and belt was off. Seems a “pulley” broke....see pics
why would that happened? Just need replaced that “pulley”? Cause damage to engine and that’s why oil out??
The pulley broke either because it was just it's time, or possibly you leaned hard on it by accident while you were down there. Check your other pulleys really well while you're at it. The belt looks like it pretty much stayed in position so I'm not sure if the pulley/belt has anything to do with the oil. The only thing that's nearby would be the remote oil filter and lines - check those out. Otherwise, it's a completely unrelated incident. Did you do any other maintenance recently?