At a basic physiological level, how is this occurring?
Every day, your body builds up and breaks down muscle. Under homeostasis, this breakdown evens out the buildup and there is no net-muscle gain. Training hard and eating properly provides the stimulus to gain more muscle than you initially had.
Once you take away the training stimulus, your body will still be building and breaking down muscle, however the breakdown will exceed the buildup, and you'll have a net-loss of muscle. This loss is faster the more nutrient-deprived you are. The loss of muscle mass seems to be mediated by an increase in protein breakdown. To cite1:
The majority of studies have inferred an increase in protein degradation through the measurement of genes associated with specific protein degradation pathways.
Note that the above discussed muscle loss is known as disuse-induced muscle atrophy1. Another form of atrophy, known as sarcopenia, which is associated with aging, is thought to have different pathophysiological aspects3:
... loss of individual muscle fibres associated with the loss of motor units, and a concomitant reduction in muscle ‘quality’ due to the infiltration of fat and other non-contractile material
Are the sarcomeres (containing myosin and actin) used as fuel by your body and expelled?
Some of it likely is, to cite2:
Skeletal muscle proteolysis can provide amino acid substrates for glucose and glycogen formation, notably glutamine and alanine. Alanine is released into circulation and reaches the liver, where it serves as an excellent substrate for gluconeogenesis.
Besides turning amino acids into glucose, the body can, among other things, reuse amino acids to build other proteins.