@mediocreplayer The analysis of a sticky valve is to first check cleanliness (dirt/damage/distortion - thank you Ivan) and proper lubrication, then comes the interface finger position to valve stroke. Proper lubrication means BONE DRY VALVES AND CASINGS, then oil to create isolation between them. Oil floats on water so drying first is a real part of oiling.
Sometimes we can hone the valves (with a loss of compression) until they work or push the player to change hand position and play with the tips of their fingers.
I have only had issues with used instruments broken in by someone else.