Step 1: Think physically about what the sign requires: a detached bone fragment must be able to sink under gravity, which is only possible inside a cavity filled with thin fluid and no solid tumour matrix or thick septa.
Step 2: A simple (unicameral) bone cyst is a single fluid-filled cavity. When it fractures, a chip of its thin wall breaks off and gravitates to the most dependent part of the cyst, producing the fallen fragment sign. This appearance is regarded as diagnostic of a simple bone cyst.
Step 3: Rule out the rest: osteosarcoma and adamantinoma are solid lesions through which nothing can fall; an aneurysmal bone cyst is multiloculated with blood-fluid levels rather than one open fluid space, so a fragment cannot freely descend. The classic teaching ties the sign to the simple bone cyst.
\[\boxed{\text{Simple bone cyst}}\]