Some fossil bones get permineralized or even replaced by minerals like silica dioxide. These tend to be somewhat heavier than "green" bone.
A bone is said to be "green" if, when you hold a flame to an edge, a smell of burning hair is produced. That is the collagen in the bone cooking. No smell, no collagen.
Some bones remain unchanged except for losing their collagen. What's left then is a crystalline latticework of the original calcium hydroxyapatite. Bones of the European cave bear, Ursus spelaeus, are an example of this sort of preservation. The bones are light-weight and inelastic or friable, but they are fossils.