Annulment of a foreign passport: what to do

I learned that a foreign passport can be annulled if it is lost, damaged, if my personal data has changed, its validity period has expired, or there is an error in the document. I am interested, if my old passport has a valid visa and the passport has already become invalid, can I somehow use this visa for travel, for example, together with a new passport, or do I need to apply for a visa again? How should I act correctly in such a situation to avoid problems at the border?