What is the definition (historically), for lost flying for “untriggered reassignment”.

Scenario is; your flight is running late. Scheduling breaks your trip and assigns your connecting flight to reserves to keep it on time. Now, you get reassigned to other flying and deadhead and says it is not an untriggered reassignment, when; you could have stayed on your original pairing ( albeit a couple hours late).

So does schedule integrity (on time) protect the company from untriggered reassignment pay?