Does zakat become void for money on which its zakat was not paid for ten years, and then its owner repented, especially if the money diminished and he started paying zakat on the small remaining amount?

Zakat becomes obligatory on wealth when it reaches the nisab (minimum threshold) and a hawl (full lunar year) passes over it. This Zakat is not waived because it is a right of the poor. It is incumbent upon the man to pay Zakat for every year in which the wealth reached the nisab. He can estimate and pay what clears his liability.