I am in the process of doing my UIM and LIM gaskets and during disassembly I have found this situation. This is on the rear of the UIM for orientation. The large hose goes to the brake booster, but the small hose is missing, and all that is left on it is a dried up old piece of hose or fitting. Where is this vacuum destined for?

That vacuum line will run across the back of the engine in a small loom by itself, somewhere it will probably go into the main loom and then down to the vacuum canister and from there is used by the HVAC system in the car to move the doors etc in directing airflow.