A picture frame with one loose corner might still look fine hanging on the wall, but that small amount of give is often a sign that the whole structure is weaker than it appears. Left unfixed, the joint tends to work itself looser over time, until eventually the frame comes apart and the picture or glass falls out unexpectedly. A quick repair at the first sign of movement avoids that risk altogether.
Take the frame down and examine the loose corner closely, checking whether it's held together with small nails, glue, or a simple mitre joint. Gently separate the joint if it's already partly open, and clean away any old, crumbling glue or dust that has built up inside the gap over the years.
Reinforce the corner properly
Apply a small amount of wood glue into the joint, working it in with a thin tool such as a toothpick so it reaches every part of the gap. Press the corner back together firmly, checking that the frame still sits square and hasn't twisted out of shape during the repair.
Hold the corner in place with a strip of tape or a small clamp while the glue sets, since even a slight movement during drying can weaken the finished joint. Leave the frame flat and undisturbed for the full drying time before hanging it back on the wall.
A properly reglued corner is often stronger than the original joint, especially once it has had time to cure fully. This small repair keeps a favourite picture safely displayed, rather than risking a fall and possible damage to the glass or the picture itself.