In the trade we commonly use a tool called an internal nipple wrench. The internal nipple wrench looks like a short, round metal punch with a rotating cam near the end. The punch tip is inserted into the pipe until the cam is inside, then the punch is rotated. As it rotates the cam swings out and wedges the wrench against the inside wall of the pipe. You then use an ajustable wrench to turn the nipple wrench to unscrew the damaged nipple or pipe section out.
You should be able to access the broken piece of pipe through the small hole in the sheetrock without opening the wall.
Nipple Wrenches (See Illustration Below) are made in 1/4, 3/8, 1/2 and 3/4 inch sizes.
The can be purchased at Plumbing supply stores, most hardware stores or home supply centers and average about $10 each.
There is also another method you might try before resorting to buying a specialty tool.
PVC is a very soft material. Find a large flat screwdriver with a tapered tip that is slightly wider at its widest point than the inside diamter of the pipe. Slip the tip of the screw driver inside the pipe until the taper is tight against the pipe, then carefully tap the screwdriver a couple times to drive it into the plastic, then unscrew the pipe with the screw driver.