It is possible for the muscles of a joint to become too flexible. According to SynerStretch, there is a tradeoff between flexibility and stability. As you get "looser" or more limber in a particular joint, less support is given to the joint by its surrounding muscles. Excessive flexibility can be just as bad as not enough because both increase your risk of injury.
Once a muscle has reached its absolute maximum length, attempting to stretch the muscle further only serves to stretch the ligaments and put undue stress upon the tendons (two things that you do not want to stretch). Ligaments will tear when stretched more than 6% of their normal length. Tendons are not even supposed to be able to lengthen. Even when stretched ligaments and tendons do not tear, loose joints and/or a decrease in the joint's stability can occur (thus vastly increasing your risk of injury).
Once you have achieved the desired level of flexibility for a muscle or set of muscles and have maintained that level for a solid week, you should discontinue any isometric or PNF stretching of that muscle until some of its flexibility is lost (see section Isometric Stretching, and see section PNF Stretching).