There is a natural "hole" in the lower mandible that can easily catch on toy parts or other things in the bird's environment. I lost a cockatiel some years ago the same way - but this was on a toy that hung from the cage by a tiny "key" ring. I also lost an indian ringneck once, whose foot became tangled in frayed rope threads on her Booda perch.
Always make sure there are no openings, sharp pieces, frayed rope, etc... on any toy parts that can injure a bird. Examine all toys every time you clean the cage, and dispose of/fix them right away - it may save your bird's life!!!