Final answer:
The supraspinatus tendon is most likely ruptured in the given scenario, which would allow dye to leak into the subacromial bursa during an arthroscopy. The correct option is D.
Step-by-step explanation:
The elder patient's complaint of shoulder pain and difficulty in arm abductions, followed by an arthroscopy where dye leaked into the subacromial bursa, suggests a potential rupture of one of the four rotator cuff tendons. Given the options provided and the anatomy involved, the tendon likely to be ruptured is the supraspinatus tendon.
This tendon is responsible for initial arm abduction and can become pinched and inflamed, leading potentially to tearing away from the bone due to repetitive motion or injury.
Therefore, the correct option is D.