Does zakat become void for one who possesses zakatable wealth but is unable to grow it or work, has no rights such as healthcare and education, and whose payment of zakat would deplete his wealth, making him like one whose money has been stolen?

Zakat is an obligation upon whoever possesses zakatable wealth. It does not cease to be an obligation due to one's inability to grow their wealth; rather, it increases wealth and blesses it. It is permissible to give zakat to those entitled to it from among the poor and the needy, even if they possess a nisab that is insufficient for their basic needs.