Is Zakat obligatory on a saved amount that has not increased for 9 years, and its owner no longer has income, and nothing will remain of it after paying its Zakat, knowing that it is saved for Hajj and for need, and amounts to 1300 Kuwaiti Dinars?

For zakat (definition) to be obligatory on monetary wealth, it is conditional upon reaching the niṣāb, complete ownership, the passing of a ḥawl (one lunar year), and that the niṣāb be in excess of one's basic needs. This saved money (1300 Kuwaiti Dinars) is in excess of basic needs, as indicated by its being saved for nine years and the children bearing the expenses. Therefore, zakat is obligatory on it, as it has reached the niṣāb (equivalent to 85 grams of 24-karat gold), and zakat is to be paid on it for every year that a ḥawl has passed, as long as it continues to meet the niṣāb.