Maintaining strength while in a calorie deficit is a good question because it affects athletes in many sports, not just weight lifters and recreational lifters training to get in better shape.
There had been much research on the possibility and potential to gain strength while in a calorie deficit.
Studies consistently found that a calorie deficit slows down gains in lean body mass.
However, body re-composition was seen possible in some situations, but as a general rule, it is significantly harder to gain muscle mass.
The more significant the calorie deficit, the longer you've been in in the deficit and the leaner the individual found that muscle growth can be hindered by as much as 500 calories under maintenance.
As a result, most people shouldn't anticipate gaining muscle when they're in a deficit. Instead, they should focus on losing fat. Any muscle you gain while losing weight is a lucky bonus.
The good thing is that other studies found that when the calorie deficit is small, strength gains were possible.
Getting stronger and growing in muscle size are two different things.
The number of calories you eat is one of many things that affect strength gains.
Most of the time, calorie deficits are set between 15% and 30%.
Remember that people severely overweight can certainly manage more significant deficits (and they are less likely to lose muscle while dieting).
To prevent muscle loss, lean individuals attempting to become even leaner should maintain a smaller caloric deficit.
When the deficit is significant, especially when it's been big for a long time, it gets harder to stay strong.
Also, losing body weight makes it harder to keep up strength. That makes sense since many strength sports have weight classes to ensure fair competition.
Ultimately, you can put on the most muscle when you are in a calorie surplus.
A typical surplus is 10% to 15% over maintenance.
People who want to gain muscle without gaining too much fat should aim for a 10% calorie surplus.