It seems to be the consensus that on a cut you should not change your training program and continue to lift heavy. Although it is also commonly stated that the body cannot gain muscle and loose fat at the same time.
How can a 5x5 program such as starting strength or strong lifts work on a calorie deficit? In theory you shouldn't be able to progress at all since your body does not have the calories to add muscle? Do people just stay at the se weight during the cutting phase?
The presuppositions in this question are mistaken. A) It is possible to gain muscle and lose fat at the same time if the conditions are right. B) It's not true that one should not change one's training program while cutting--one should still do some heavy lifting, but the program should change.
The point of heavy lifting during a cut is to maintain (or lose as little as possible of) lean muscle or one's level of strength.
It is indeed possible to gain muscle and lose fat, sometimes. Many novices do it, and some people find it possible in other training scenarios. It's hard, it can't always be made to work, but it happens.
If you're trying to run a hypertrophy/strength program like SS or SL while not eating enough, you will hit walls faster than if you were eating enough to grow. That might be okay for you or it might not.
