To properly assess this safety issue, a distinction needs to be made: flexibility in joints is a different matter than flexibility in muscles.
The job of ligaments is to help hold a joint in alignment, yet still allow for normal range of motion. If a ligament is over-stretched, then it is unable to stabilize the joint as well as it did before. The joint becomes more vulnerable to injury unless adequate muscle strength is developed to compensate for the extra looseness.
If the ligaments are stretched sufficiently — either from a sudden impact (such as a fall or impact), or over time (by overstretching them bit by bit) — the joint will be injured. There will then be inflammation and pain in the joint, for inflammation is the body’s mechanism for stabilizing the compromised joint.
The body can repair ligaments to a certain degree, but due to the low blood supply to the ligaments, as well as to the nature of the tissue they’re composed of, repair is slow and they are usually unable to return to their original state. To bring stability back to the joint, the supporting muscles then need to be built up more than usual in order to compensate for the stretched ligament(s).
Therefore, in yoga or any other activity, care should be taken never to stretch the ligaments. Dr. Garrick states in another of his books, Be Your Own Personal Trainer:
You should never feel the stretch in your joints. It’s virtually impossible to stretch joints. Stretching joints means stretching ligaments, and ligaments aren’t particularly elastic. They have a tendency to tear rather than stretch.
One indication that a joint is being stressed (therefore potentially overstretching the ligaments) is if there is any sensation inside the joint itself.