Dear hixt,
Do you have the 1997 Tiburon rear brakes shown in this picture?
You mentioned brake calipers and brake shoes, so I was confused.
To clarify, disk brakes have a rotor, a caliper, and an inner and outer brake PADs.
Drum brakes have a drum, a small little slave cylinder at the top of a backing plate, and front-side and back-side SHOES.
From what I can tell, I THINK you have the 1997 Tiburon with the rear disc brakes so this write-up assumes disc brakes.
The part you think is fused (has the rubber boot on one end) is the rear brake piston?? The problem is you forgot or did not know that the parking brake engages through the rear brakes by a ratchet that grips the side of the brake piston. The piston must be backed into the brake cylinder bore with a Hyundai special tool.
If you don't have this special tool, you can use long-nose vice grips on the piston body to rotate it back in the bore IF you plut electrical tape or duct tape on the jaws to prevent scratching/scarring the piston outer surface.
Unless the part that is fuzed is the lower guide rod. A new guide rod is available at Autozone or most auto parts stores. Go buy the new guide rod first. It should come in a kit with 2 guide rods, 2 rubber boots, and 2 bolts. Once you have a replacement in hand, you can use vice grips and a rubber mallet to pull the old guide rod out.
Byron