If one is unable to throw away one's possessions, they are owned by their possessions.
"If one is unable to throw away one's possessions"=「自分の所有物を捨てることができないと」
"they are owned by their possessions"=「彼らは自分の所有物に所有されている」
Example in context:
"I know I should throw away my things, but I can't seem to let them go. Now they are owning me!"