Extensor tendons are on the back of the hand and are responsible for straightening your fingers, thumb and wrist. The tendons are connected to muscles that attach by the elbow. When you contract the muscle, it will pull on your tendon to straighten your finger. An injury to an extensor tendon may cause your finger to droop. Injuries can happen when the tendon is cut. The tendon can also break or tear after a forceful injury. Treatment includes splinting the finger straight for several weeks or surgery.