Final answer:
The transversus abdominis is the muscle layer in the paralumbar fossa without a distinct sheath, which forms the deepest layer of the abdominal wall. This muscle is crucial in spinal and hip movements even without a separate sheath due to its connections to other structures.
Step-by-step explanation:
The layer of the paralumbar fossa muscle layers that does not have a sheath is the transversus abdominis. This muscle is part of the abdominal wall and forms the deepest layer. The skeletal muscles, such as the latissimus dorsi, are covered by three layers of connective tissue collectively called the mysia. These layers may fuse with other structures such as tendons, aponeuroses, or fascia to facilitate movement of the skeleton. However, in contrast to rectus abdominis which is covered by the rectus sheath, the transversus abdominis in the paralumbar fossa does not have a distinct sheath.
The connective tissue sheaths play a critical role in transferring the force generated by muscle contraction to the bones. When the muscle fibers contract, the tension is transferred through the mysia to these structures, eventually pulling on bones to cause movement. Despite the absence of a distinct sheath surrounding the transversus abdominis, it still plays a significant role in lumbar spine and femur movements by connecting to other structures.