End caps and other laminate edges sometimes come loose and can get broken off if not reglued, but as long as the particleboard backer is in good condition, the fix is simple. Scrape off chunks of debris or dried lumps of glue from the end cap. If the countertop is newer, first try to iron the end cap back on with a medium-hot iron to reactivate the glue. However, in most cases the loose piece will need to be reattached with contact cement.
Sand rough areas with medium-grit sandpaper, then apply the contact cement (Photo 1). Open nearby windows to dissipate the fumes from the glue. After both sides are completely coated, keep them separated with a toothpick (Photo 2) until the adhesive is tacky. Carefully rejoin the two sides, starting at the back of the glued area (Photo 3). Contact cement bonds instantly, and if the wrong areas accidentally touch, you'll have great difficulty pulling them apart.
Finally, rub away any dried glue around the edges with your finger.
Note: If your end cap has broken, scrape it off and take a piece to a home center to find a matching replacement piece.