Final answer:
The ligament that connects the head of the femur with the acetabulum during a hip dissection is the ligament of the head of the femur. It carries an essential artery to the femur's head, and a fracture could lead to avascular necrosis due to compromised blood supply.
Step-by-step explanation:
During a chicken thigh and hip dissection, if the hip bone is dislocated, the ligament that connects the head of the femur is known as the ligament of the head of the femur. This ligament is attached to the fovea capitis on the medial side of the femoral head and spans to the acetabulum, although it is considered weak and provides minimal support to the hip joint. It does, however, carry an essential artery for the blood supply of the femur's head.
A potential consequence of a fracture of the femoral neck within the hip joint capsule could compromise this blood supply, leading to avascular necrosis of the femoral head. This is because the ligament of the head of the femur carries an artery, and damage or disruption may impair blood flow.