It is supposed to slide freely up and down with the quill. It's supposed to keep the slot where the quill lock nut/scale is closed when the quill is down. Without that sleeve the bearings and spline are open to the elements.
There are two tabs on the sleeve, can't remember if they are on the top or bottom, they're supposed to sit or lock into the quill to slide freely with the quill. If it's not, it's either not oiled, or the tabs aren't where they're supposed to be, or they're broken off.
Pull up a quill exploded view. All the clones are all the same. In fact, they're so close to the Bridgeport that OEM Bridgeport parts fit.
My First milling machine, a Taiwanese mill, has a whole bunch of real Bridgeport parts for the power feed I installed way back.