This may be another one of those "Duh!" scenarios where research proves the obvious like, "study shows placing hand on hot stove causes burns".
Nevertheless, much of the time we don't make the practical application connection to things that we usually ignore, and for exercise management, fatigue is often viewed as something to conquer by pushing through it rather than resolving through rest, or perhaps by putting a piece of tape on your muscles.
DOMS; delayed onset muscle soreness.. your muscles feel stiff and sore in the days following exercise. A study in the journal Medicine & Science In Sports & Exercise (1) showed that 48 hours after training muscles with DOMS had a strength reduction of about 21%. While this has training implications (do you need to rest until you return to full strength before considering training again?), there was another interesting finding.
The study concluded, "Reflex activity in leg muscles elicited by rapid destabilizing perturbations is reduced after exercise-induced muscle soreness."
Translation, you will have less functional stability. Your ability to respond to high stability demands like playing sports will be reduced, which would increase your risk of injury.
While recovery days can include light or moderate exercise, it's not a good idea to train hard with weights, then play hard in sports the next day.
In another study, this time from the journal Gate and Posture (2), researchers found placing a piece of tape on the ankle of fatigued study subjects allowed them to maintain ankle control. When no tape was applied, fatigued subjects demonstrated "degraded postural performance", they lost balance more easily.
How does this work? Researchers suggest that local muscle fatigue impairs the ability to send relevant postural position information to the brain, and that the skin, if stimulated, can take up the communication corridor slack.
Does this mean we should keep training and simply tape up our skin to maintain coordinated movement? I wouldn't go that far. There is still muscle recovery that requires more time to recover from, and there might be a problem with masking reduced coordination as it may prompt people to train weak and unrecovered muscles, but this information can help therapists and coaches understand and design appropriate recovery protocols.
(1) Delayed-Onset Muscle Soreness Alters the Response to Postura... : Medicine & Science in Sports & Exercise
(2) Degraded postural performance after muscle fatigue can be compensated by skin stimulation