If one end of the hose is attached to the duct that goes from the air filter box and the throttle body and the other end is going to a port in the valve cover, then this hose supplies filtered air to the engine to make up for the air drawn out by the PCV valve.
There are holes in the edge of the head that go all the way down to the crankcase. There allow oil that is pumped up to lubricate the valve train drain back into the crankcase. Any oil fumes will generally rise up and collect under the valve cover.
The PCV valve sucks these fumes into the intake manifold where they go into the engine to be burned and expelled. This hose supplies replacement air that has gone through the air filter so that the crankcase and valve cover don’t develop a vacuum.
It should have no affect on the idle of the engine. Maybe in an LPG engine, somehow the propane that has vaporized is getting upstream of the throttle body and into this hose. When you disconnect it and the engine is running, can you smell propane gas coming from the hose?
If this hose is blocked up at the duct, then that could be what is happening, the crankcase and valve cover are developing a vacuum. If that is the case, that hose would be hard to remove when the engine is running.
Anyway, I am not familiar with how LPG is introduced into the airstream for the engine.
Is this engine one that has both systems where you can switch between LPG and regular gas? If so, do you have this problem on gas?