In stretching, there are two reflexes at work, which are actually the fastest reflexes there are because they are relayed over the fastest (thickest) nerve fibres in our body (Type I a/b sensory and delta-motor fibres, with 50-100 m/s):
- The muscle spindle reflex: Triggered by proprioceptors embedded drectly into the muscle, they react to force within the muscle. When a muscle is stretched (relatively fast), it reflexively contracts in order to protect itself from overstretching/taring apart. This part is the differential proprioception, ie. it measures a velocity. There is also a slower type (going over sensory Type II and gamma-motor neurons, 20-50 m/s) that measures the length (via proportional proprioceptors) and hightens the tone according to the length, ie. the longer the muscle becomes, the stronger it will tense up against further lengthening. This is what you mainly work against when stretching.
- The Golgi-Tendon-Apparatus: This reflex works antagonistically and depends on proprioceptors directly embedded into the tendon and is supposed to prevent tendon injuries. When the tendon is experiencing too much tension, two things happen: Through one path, the stretched (but contracting, see above) muscle is neurally inhibited, ie. the tone is lowered, allowing for further lengthening. At the same time, the antagonistic muscle is excited, ie. you start to activate the counter-movement in order to take tension from the muscle + tendon.
Now, why tendinopathy and why near the butt, exactly? There is an intricate interplay between the two (or four, depending on the perspective) reflex mechanisms above, constantly regulating your muscle tone. What you do in yoga is stretching the ischios (back of the thighs) almost exclusively from the proximal lever, ie. you bend the hip with straight legs. This means that you got an extremely long lever (the legs) and extremely strong muscles (hip flexors), often supported by gravity, pulling mainly from the proximal tendon, ie. from your butt bones, with the muscle spindle reflex(es) constantly working against the stretch by pulling the muscle short. It is only natural that the tendon, with one side (bone) being pulled away by strong muscles and the other side (muscle) pulling away as well, is the first place where tension-loosening-further stretch will take a toll. The Golgi Tendon Reflex will try lower the load, basically by sending inhibitory potentials into the motor neurons but this cannot fully compensate conscious effort to stretch further, which excites those neurons.
Basically, the take-away message should be never to stretch into actual pain. It triggers the contraction reflex and makes you ultimately work against your sinews, not your muscle. There should be a sensation and it does not have to be pleasant, yes, but not actual pain.
Also, it is often advised to stretch the ischios by active extension of the knee (ie. both hips and knee are extended from an appropriate pre-tension with bent knee), exactly because it has a lower toll on the sinews due to antagonistic inhibition as a moderator and the tension being dispersed more evenly over all sinews.
As of what to do against the injury: moderate, isometric loading in neutral joint positions is generally the gold standard.
Regarding the comatose/full anaesthesia part
What you describe is used in a surgical procedure called arthrolysis. Since the muscle fibres do not get any signal and they need a depolarisation of their membranes in order to contract, the muscles only give their structural elasticity (titine within, and mainly connective tissue outside of the muscle fibres proper) as resistance against elongation. No base tone nor any reflexes work here. You get the wrong idea, though:
- The procedure produces immense post-surgical pain. Any existing adherences are literally torn apart, producing structural damage and inflammation around them.
- It often leads to bad outcomes since the muscles still "lock" in their old ROM when awake.
What stretching routines do is desensitiving the muscle spindle reflex(es) (first and foremost) and only in extreme, pathological conditions they also rip actual significant adherences apart (either between connective tissue or surplus titine in the fibres). Your joints as such have a great ROM, it's just that your muscles are no taught that it is safe to go there. Another fact that is often forgotten is that it is not even physiologically wanted to be overly flexible since the muscles are not able to stabilise the joint in extreme positions since their strength is significantly reduced (because not nearly as many myosin-actin connections can be established due to smaller overlapping zones in the sarcomeres). Also, ligaments once slacking due to repeated, extreme joint positions lose function (stabilisation and arthrokinematics) as well.