Once the muscle fiber is at its maximum resting length, additional stretching places force on the surrounding connective tissue. As the tension increases, the collagen fibers in the connective tissue align themselves along the same line of force as the tension. Hence when you stretch, the muscle fiber is pulled out to its full length sarcomere by sarcomere, and then the connective tissue takes up the remaining slack. When this occurs, it helps to realign any disorganized fibers in the direction of the tension. This realignment is what helps to rehabilitate scarred tissue back to health.
When a muscle is stretched, some of its fibers lengthen, but other fibers may remain at rest. The current length of the entire muscle depends upon the number of stretched fibers (similar to the way that the total strength of a contracting muscle depends on the number of recruited fibers contracting). According to SynerStretch you should think of "little pockets of fibers distributed throughout the muscle body stretching, and other fibers simply going along for the ride". The more fibers that are stretched, the greater the length developed by the stretched muscle.
The nerve endings that relay all the information about the musculoskeletal system to the central nervous system are called proprioceptors. Proprioceptors (also called mechanoreceptors) are the source of all proprioception: the perception of one's own body position and movement. The proprioceptors detect any changes in physical displacement (movement or position) and any changes in tension, or force, within the body. They are found in all nerve endings of the joints, muscles, and tendons. The proprioceptors related to stretching are located in the tendons and in the muscle fibers.
There are two kinds of muscle fibers: intrafusal muscle fibers and extrafusal muscle fibers. Extrafusal fibers are the ones that contain myofibrils and are what is usually meant when we talk about muscle fibers. Intrafusal fibers are also called muscle spindles and lie parallel to the extrafusal fibers. Muscle spindles, or stretch receptors, are the primary proprioceptors in the muscle. Another proprioceptor that comes into play during stretching is located in the tendon near the end of the muscle fiber and is called the golgi tendon organ.