You certainly can overstretch a muscle (and injure tendons) by stretching past the point of comfort. The signs of over stretching are: discomfort past a point in the range of motion, tightening of the muscle in the response to pushing past the normal ROM, and soreness after stretching.
It’s pretty simple to avoid over stretching by paying attention to how you feel as you stretch, easing up on a stretch that feels uncomfortable and taking plenty of time to move into a deeper stretch.
Over stretching is just like over training. You shouldn’t stretch beyond a slightly uncomfortable tightness. You shouldn’t stretch beyond a joints safe range of motion. You shouldn’t stretch “cold”. There is a point at which more stretching will not yield further gains in ROM without tissue damage. There is a a limit in how long you want your muscles and tendons to be stretched to for performance and safety.
The number of people who intentionally over stretch is very small though. The vast majority of people do not stretch enough or properly.
Yes, you can over-stretch. For example, one of the dangers of conducting PNF stretching can be overstretching to the point of injury if you are not very careful since this technique basically overcomes your body’s natural stretch reflex.
I hope this helps.