Although it is not the most-used muscle when working the back, the long head of the triceps brachii is the most frequently injured muscle during back lat pull-downs with heavy weights or during chin-ups with added weight.
The latissimus dorsi is a powerful, fan-shaped muscle that attaches the arm to the rib cage, and whose distal tendon is strongly attached to the humerus. This is the main climbing muscle. The long head of the triceps brachii, on the other hand, is a similar muscle whose main function is to extend the forearm and secondarily to bring the arm toward the ribcage. In this way it complements the action of the latissimus dorsi.
Tearing of the long head of the triceps occurs when the muscle is fatigued, most frequently after an improper warm-up. It only takes a sudden relaxation of the latissimus dorsi during chin-ups with added weight to immediately shift the tension to the long head of the triceps.
This tendon my partially tear, most often close to its insertion on the scapula. (fortunately complete tears are infrequent)
Unlike incapacitating shoulder injuries, which may completely halt upper-body training, a tear in the long head of the biceps is less devastating. You can still perform back exercises such as seated rows or T-bar rows and movements for the triceps such as forearm extensions at a high pulley with the elbows next to the body despite the injury as long as you begin with lighter weights.
However, a brief rest period is recommended before beginning upper-body training.