Non-possessiveness of mind/body/self does not mean self-neglect or self-abandonment. In some forms of mental illness, known as dissociation, people disown their thoughts or memories. Sometimes people may even disown part or all of their body.
"Despite incontrovertible evidence, some people have even been known to deny that the disowned limb is attached to them, and others have begged for surgical amputation of body parts that do not fit into their internal sense of self."
New Scientist, 13.9.2003