That big pulley "may or may not" stick to end of crankshaft; BUT "more often than not" BOTH damper and pulley come off together, because of paint and rust on bore of vibration dampers' inner hole.

I've had to remove both, "as a unit" , use wire brush(on die-grinder) on stub shaft of the pulley, and put a short 4x4 wood block vertically, on floor, and flip that hold assembly over wood block and "bang" the stub shaft portion on wood block, while I lift and lower(bang) ; holding the vibration damper. Note: due this low to the ground, because when everything comes "loose" that expensive pulley might fall and break a belt pulley sheave, if it hits the ground or concrete. Maybe do this above some cardboard or old carpet.

Now, if that damper has been changed once before, then it will likely come off easy.

Note: If the pulley and damper separate, easily, on the engine; we would take an old damper bolt, with its bolt head ground off, and thread it into the crankshaft, because we don't want that expensive big pulley dropping to the floor, if the little bit of rust breaks free, on end of crankshaft. I'm just warning you, that big pulley can break loose at any time, and drop = you need to be aware and prepared for this.

I've had to two pieces, seem stuck together, but has I carried them from engine to work bench, they "broke free"  = this is one reason we tend to leave at least one long bolt, thru the assembly, until we get it over to work bench or down to the floor( usually go to the floor, because it can't fall, if it is on the ground)