Think of what really happens: The eccentric describes the external observation of the movement taking place but when muscles contract they shorten. Thus the muscular contractions are still concentric in nature. An eccentric contraction describes an eccentric motion (negative) where the muscle fires concentrically enough to prevent free fall. In other words, if you're doing an eccentric squat you use enough positive tension (concentric firing) to control the weight on the way down.
A better name for eccentric strength IMO would be eccentric control, since control is all that is really happening.
when a muscle is lengthened and contracts under tension a stretch is likely to result, which explains why eccentrics are more damaging. When a weight can't be controlled and an involuntary stretch under tension results the result can be catastrophic. This is a problem with focused eccentrics as the proper definition of "control" is often open to interpretation.
You can lower more weight than you can raise so training with focused eccentrics is really just an attempt at supramaximal loading. A weight that can be maximally lifted concentrically will likely be too light to even challenge maximal eccentric control (depending on how you define it), which explains why concentric only training doesn't always impact eccentric strength.....it depends on the movement but in general it's not heavy enough.
However, in my experience, with very few exceptions the use of stuff like pure eccentrics is little more than an attempt by theoreticians at doing something cutting edge. The likelihood of the results being any better than any other garden variety programing is nil, and the risk of injury is greater. Plus, the ability to control a weight changes dramatically depending on what point of the movement you're talking about. Most blowtards will overestimate what they can do and when they hit the transition point of a movement (CJC) they'll lose control of the weight and will end up tearing something - or at the very least be sore for days. If you're gonna do eccentrics a better way to do them is find the maximal amount of weight you can lower and hold completely motionless for 3 to 5 seconds at the toughest part of the movement. Right at or just below parallel in the squat and right below the midpoint in the bench. Use that weight as your maximum. Your mileage may vary but that can be an effective training method and it can/does work well for deadlifts
