let's say people do 8 reps of an exercise.
my guess is that more people, of those who injured themselves, did that on the last reps, not the first.
so no i wouldnt agree that the last reps are the safest.
I can see how it would seem counter-intuitive to claim that the last most difficult reps are actually safer than the initial "easier" reps. After all, just look at our hypothetical trainee taking those 8 reps to absolute failure unable to do a 9th despite his best efforts. He's relatively cruising in the beginning whereas toward the end he's grimacing, straining and even groaning at those last few reps. It would seem obvious that in that state of great effort, the highest intensity level, he would hurt himself.
It reminds me of my days taking Physic classes how things seemed so obvious whereas in fact I was completely wrong on how things worked in nature.
The majority of injuries in resistance training is when the upper limits of a muscle or tendon tensile strength and integrity are exceeded. This can happen due to poor form and a joint is placed in a vulnerable position, say, for example, the knee is subject to a twisting type of stress rather than the bend and straighten hinge-type movement it was designed for. But since the argument is whether extreme effort, intensity, is more likely to injure someone rather than low-intensity effort we will put the issue of poor and sloppy form aside for now though it is absolutely correlated, though not limited to, with the intensity of effort.
The reason for this is the relationship, rather the inverse relationship, between force and intensity. The force generated in moving the weight in the course of a set, and the intensity, the cognitive and physical effort, required to move that weight as the set progresses.
Taking our example of a person performing eight reps to absolute failure, with say, 200 lbs, unable to do a ninth rep despite his best effort. The first rep will be quite easy. He easily generates over 200 pounds and does so with ease. So during the first, and subsequent initial reps, the force is relatively high and the intensity is low. As the set progresses, as the reps start to increase, his strength starts to go down, the force he is able to generate diminishes, while at the same time his intensity increases. His intensity of effort starts to increase dramatically as the force he is able to generate, his momentary strength starts to diminish.
So since injury occurs when one generates too much force on a muscle or tendon, those last reps actually become safer because you are simply too weak to injure yourself.
Again this is only to address the safety or increased risk as it pertains to intensity of effort. It does not take into account sloppy form which can occur whether you are fresh or tired. And, of course, your form is much more likely to get sloppy as you fatigue but that just means it's sloppy form, and not fatigue per se, that causes injury. That's why that the very thing that many claim why machine training makes one more likely to get injured, you are forced into a fixed unnatural plane of motion, which is true, but it is actually the very aspect as to what makes training on a machine safer -- you are forced into a fixed and stable plane of motion.
As you fatigue during a set of squats. As the strength and force you are able to generate from your hips and thighs begins to diminish as the set progressives, you start to bend forward as the bar isn't moving up as easily so you start to bend forward, essentially crushing your body as the bar slows down or remains stationary in mid-air, folding your body in half putting undue strain on the much weaker and vulnerable muscles of the lower back. With, say, the machine Hack squat, your body and back are fixed, i.e., forced into a fixed and stable plane of motion, to remain upright and stable no matter how much stress is put your quads. The worse that would happen is that you would not be able to rise up and have to replace the pins in the lower position.
