A lot of athletes who sustain major injuries tend not to train because they feel it will decrease the recovery process. I am here to tell you this approach is backward. Any gym or personal trainer telling you that you shouldn't work out at all if you are injured; probably has no idea what they are doing or little experience.
Regardless you should not trust them as your personal trainer or fitness coach.
If you’re inured, it is very important to perform single-sided training in the non injured limb and you will minimize the effects of detraining. It is well established by most health experts and personal trainers that if you suffer an injury that causes you to be out of commission on one side, you can maintain strength and accelerate healing by continuing to train the uninjured limb.
For example, if an athlete tears a pectoral major on the left side and can't train for 12 – 16 weeks, their fitness coach or personal trainer should focus on training their right side. By performing exercises with the right arm an athlete can decrease strength loss and speed recovery due to an effect known as “Neural Muscular Cross over Effect”.
Neural muscular cross over effect occurs when you strength train a limb on one side of the body, which results in an increase in strength in the same limb on the other side of the body due to neural adaptations. It does not just work arms and legs, but NMCOE appears to be effective for all muscles including those around the ankle and wrist joints. The neural muscular cross over effect is more pronounced when the non-dominant limb is immobilized and the dominant limbs doing the work, but there is evidence it works in the opposite case as well.
Strength gains in the untrained limb are typically in the range of 10-25% depending on if that limb is dominant or not. Strength gains average around 35% and 60% of those in the trained limb. In studies that included a control group, strength gains in the untrained limb averaged about 8%, while not immediately impressive, these gains are certainly better than strength loss due to immobilization. Additionally, it appears that less range of motion will be lost in the injured limb due to the neural muscular cross over effect, a major benefit for athletes.