5th dnd – Does the destruction of the phylactery of a lich destroy the soul in it?

The entry of MM for a lich mentions the destruction of a phylactery is a difficult undertaking, but the only way to prevent a lich from breeding again and again.

Does destroying the phylactery destroy the soul? If not, is there a tradition that explains what happens to the soul of a lich when its phylactery is destroyed?

As a rule, lich phylacteries may permanently destroy or consume the souls that are provided to them by the required ritual, but it is likely that the soul of the lich does not actually belong to it as long as the phylactery is intact.

The D & D 5e answers are preferable, but the mechanics and knowledge of other related systems will be noted as guidelines if anything in the 5th does not exist on the subject.