Final answer:
The structure in question is likely the suspensory ligament of the axilla, part of the clavipectoral fascia in the anterioinferior part of the axillary region, providing structural support to the axilla and allowing passage for neurovascular elements into the upper limb.
Step-by-step explanation:
The hard tube-like structure that you can feel in the anterior axillary folds most likely corresponds to the suspensory ligament of the axilla, which is indeed a part of the clavipectoral fascia in the anterioinferior part of the axillary region. This fascia extends from the clavicle and the coracoid process downwards. The pectoral girdle, consisting of the clavicle and scapula, has various ligaments that stabilize it, and the suspensory ligament is one such structure that works to support the axillary structures including the axillary vein and artery, as well as provide passage for neurovascular elements into the upper limb.
The clavicle, through its articulations and ligaments, plays a key role in the framework of the shoulder region. It transmits forces from the upper limb to the axial skeleton and assists in the protection of underlying neurovascular structures. Given your description, it is less likely that you are feeling the tendon of the pectoralis major, as it is not tubular and does not extend as inferior as the structure you're describing.