In last few days of injury. FAQ explains injuries.

From the FAQ:-

My player is injured but I can still put him in the formation. How can that be?
Injured players can play if they have less than 7 days of rehabilitation left. Keep in mind though that an injured player won't play to the maximum of his abilities.
If the player still has from 4 to 6 days left he will play with 60% to 70% of his ability
If the player still has from 2 to 3 days left he will play with 71% to 80% of his ability
If the player still has 1 day left he will play with 81% to 95% of his ability

When on the 4-6 range, he will show as bad, 2-3 will show a good and 1 will show as very good.

Nothing to do with rest. A player automatically heals 1 day per day. fitness centre and docters allow quicker healing.