I see it a lot on Chins and Dips where I am able to move a lot of weight for a desired protocol of reps/sets, but in moving the load, I feel like I'm going to injure myself. It's hard to quantify but I'll give it a shot. Using Chin-Ups as my example, I can move a good amount of weight, last week BW+45 for 5x5. Lifting is often painful but getting strong often rewards you with a heightened pain-tolerance. That said, do you ever feel that sensation that pulling harder will rip your tendons off the bone? I was doing Chin-Ups for BW+50 for 5x5 but on the 4th set, I got that "tendon strain" feeling and called it, to be safe. I knew I could finish all the reps, but I don't want an injury. What do you do when you know you are strong enough to do your lift, but you get that sensation that you will injure yourself in the process? Chins have that ability to let you move more weight as long as you just pull harder, but you can end up hurting yourself. Is there a weak link in there somewhere? I see two solutions. Change a rep range, or deload down to a less strenuous weight and work back up, to hopefully fill any holes. I'm not complaining, I just need perspective. Also, I find that not doing those "grinder" reps on my presses keeps me from burning out, but can one make strength progress without doing those grinder reps? Does the lift fail when the bar slows instead of when form breaks or the bar cannot be locked out? What I mean is usually I will consider it progress to complete all reps, even if the last ones are a war, thus possibly damaging myself and requiring longer recovery. Would progress still be met if a lifter didn't work much beyond the weight that slows his lift speed?
I've never had the feeling that I was about to pop a tendon or even pull a muscle. Muscle pulls just seem to come out of nowhere for me. Maybe I'm just ignoring the sensation, but I've never been in the middle of a hard rep and thought if I continue it feels like I could rip something, UNLESS I'm already injured and trying to train through it. As far as your last paragraph, I really think you need to strain against heavy weight to get much strength stimulation. I really wish all it took was lifting lighter weights fast until they slow down. Louie Simmons and Westside would not have accomplished what they have if that is all they did. I think more credit should go to their max effort days, and the way they change exercises around, than the DE method. Sure it plays a role, and increases the effectiveness of their whole approach, but I don't think its the main reason for success.
If you are ever going to get beyond pedestrian strength, you will have to get good at "fighting the weight", which means to push as hard as possible, even when the bar shows no movemement, and all the while maintaining near perfect form. Some folks call these grinders, and its not that you have to do that all of the time, but at least some of the time. The real key is to maintain the form, when a bar stalls, its easy to shift around, change your biomechanics ( ie, try to cheat it up) which can open you up to injury. The best way to maintain good form during a tough rep is to ALWAYS maintain near perfect form on each and evey rep, including the warm-up. I have often said that when I am doing a set of ten, what I am really doing is ten consecutive singles. I will give you a fast example of something I see all of the time. A guy is doing a tough set of 8 reps on the bench, he does the first seven and then he goes for number eight, but instead of push straight up to lockout, he begins pushing back towards the uprights essentially racking the bar on the last rep--big, big mistake, every rep should look like every other rep, I see this where guys do the last rep on a set of squats and before they are completely standing up, they begin to walk the weight forward into the rack. Bad habits breed Bad Habits, and if you cheat when the reps are "somewhat easy" it will lead to cheating when they are hard and need to be fought in the correct way.
That's a good point. Uncontrolled movement under extreme physical stress is an easy way to pull something. As for the original question, I have nothing useful to add other than that you have to push your limits from time to time, with those reps that you call grinders. I HAVE had that feeling of something being wrong and something bad being about to happen if I do a movement one more time. I usually stop there.