It is already a part of the calculation. Different types of stars have different goldilocks zones so if a star transitions between types the zone placement will be different afterwards.

If you're asking would life on a specific planet survive the transition, the answer is no, almost certainly not. Take our star and Earth as an example. It's the only one we have. In 5 billion years when our sun transitions to a red giant its diameter will massively increase but its mass will remain the same. So the planetary orbits relative to the center of the sun will remain the same. There's a good chance that the Earth will be consumed entirely. Wherever the new goldilocks zone is, you can be pretty certain that it's not inside the star.

This type of problem will be similar with most of these transitions. If the stars diameter and energy output change but the orbits of the planets surrounding it do not, it's highly unlikely that a planet would be inside it both before and after the transition. Probably impossible but I don't have the time or data to prove that.