In Japanese, the verb "ある" is used for both existence and possession. But perhaps it used to be two separate verbs.
In my research, I've discovered two kanji, "有" and "在", which mean "possess" and "exist" respectively. And guess what, their kun-readings are both "あ". So perhaps the "ある" of existence was once written ”有る” for possession and "在る” for existence. I kind of wish they still were, as it would make things clearer.