She is old but still has (full) 'possession' of her senses/faculties. [=she is still able to think clearly]
I have 'in my possession' [=I possess] silverware that has been passed down in my family for generations.
He did not have 'possession' of the ball before he was knocked out of bounds.
(..) - Forrest Gump, John Lennon. - Welcome home. Can you tell us, what was China like? In the land of China, people hardly got nothin' at all. No possessions? And in China, they never go to church. - No religion, too? - Hard to imagine. Well, it's easy if you try, Dick. Some years later, (..)1994 Forrest Gump