According to my dictionary app -ざる is the literary form of -ない and あらない (有らない/在らない) means does not posses/ does not exist depending on the kanji. So I imagine a decent translation would be “the treasure that one does not posses/have” or “the nonexistent treasure”.
According to my English copy of HP the line is “A treasure that was never yours” which tracks pretty well with “the treasure one does not possess”. So basically あらざる宝 = 有らない宝. I hope this helps!
Yah, I was about to say, but I didn’t have the time to sit down and type. It’s also archaic. Fun fact: the ~ざる is the reason why the Three Wise Monkeys are monkeys - it’s a pun, you see. Their names are 聞かざる, 見ざる and 言わざる = “do not hear, do not look, do not speak”, but ざる sounds like an aspirated 猿.
I just reached that point, and I’m currently pondering why double swinging doors are called 観音開き. Wikipedia says it’s because Kannon temples tended to have double swinging doors, but were they really that unique to Kannon temples that they became the “kleenex” of doors?