I think most popular and effective training programs do not allow you to recover fully. Recovering fully, being at peak power and endurance, is usually achieved by tapering off your training.
As such, simply by the fact that you'd taper off a training program (like 5/3/1, 5x5, etc) before a competition, it's a logical conclusion that not tapering off (ie: a normal training week) means you're not fully recovered. Rather, you're recovered enough to handle more load, and stimulate more adaptation.
Is there any scientific research that indicates how training a
particular muscle when not recovered fully affects long term
I would just comment to say that "training a particular muscle when not fully recovered" means a lot of different things. You can do it in a smart way, such as any effective training program, or you can do it in a silly way and stunts adaption and instead of leading to recovery leads to exhaustion. Scooped from the Wikipedia on stress and the general adaptation syndrome concerning exhaustion:
Exhaustion is the alternative third stage in the GAS model. At this
point, all of the body's resources are eventually depleted and the
body is unable to maintain normal function. The initial autonomic
nervous system symptoms may reappear (sweating, raised heart rate,
etc.). If stage three is extended, long-term damage may result
(prolonged vasoconstriction results in ischemia which in turn leads to
cell necrosis), as the body's immune system becomes exhausted, and
bodily functions become impaired, resulting in decompensation.
The result can manifest itself in obvious illnesses, such as peptic
ulcer and general trouble with the digestive system (e.g. occult
bleeding, melena, constipation/obstipation), diabetes, or even
cardiovascular problems (angina pectoris), along with clinical
depression and other mental illnesses.
In that case we're not talking about "exhaustion" in the sense of a tiring workout, but rather where you are (typically over a course of weeks) simply subjecting your body to more load than it is able to recover from. Beyond the load, other factors that can affect that balance include but certainly are not limited to:
- Hormonal levels
- Purely genetic differences
- Previous use of anabolic steroids