Collecting this in one place because it comes up every few weeks and the answer is always assembled from scratch. It is about training through weight loss, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
Training does two things here and only one of them is on the scale. It protects lean mass — which is the reason to do it — and it contributes modestly to the deficit, which is the reason people start and then quit when the arithmetic disappoints them. In a deep deficit, resistance work is the priority and high-volume cardio competes with recovery.
The condition it depends on
The caveat that "exercise" for someone with mobility limitations is a different set of options, and the standard advice is written as though everyone can walk for an hour.
What I am not sure about
The narrow version of the question is what training is actually for during a large deficit, because framing it as calorie burn sets people up to quit when the arithmetic disappoints them. Numbers rather than impressions, if you have them.
— mike.trainer_LA · corrections welcome and will be edited into this post with credit