If you sell the player, the person who gets them will get them injury free, but with the same morale/condition they have now

You can then get replacements. Of course they could get injured too. Maybe your players are tired because you have the arrows on, it increases stamina drain. Or possibly your opponents have hard tackling if you are much better than them

Tough run on injuries by the way, I cured a player two days ago and now my best midfielder and top scorer broke his leg in easy 6-0 league win - 20 days out