I dont really see these dom/tert and aux/inferior "loops" as loops, quite contrary, i think they are a product of this natural loop between introversion and extraversion being blocked and the person being too focused on one side.

I should define what i mean by the shadow in this case. It is basically the things that you are, but dont want to be. Pretty much the same of how freud saw the unconscious mind, some trash can of repressed thoughts, feelings, etc.
I am not talking about the shadow of 8 function theory, and i dont use the 8 function model with this. Opposing/non preferred attitude simply means E for I types and I for E types.

With introverts dom/tert loop would naturally be being stuck in the introverted attitude to escape something threatening external influence. With extraverts, it would be the introverted attitude that they want to run away from.

I see this more of an defense mechanism against the influences of the non preferred attitude.

Also i think when this sort of dom/tert defense happens, the non preferred attitude of aux/inferior starts to shadow the ego, due to ego wanting to repress the threatening impulses coming from the non preferred attitude.

Because aux function has so strong influence on the ego normally, once it starts to shadow the ego, it doesent lose that strong influence(it just causes you not being conscious of it anymore), but it now has strong negative influence and gets mixed with negative influences of the inferior. You could see it as defending against the influences of the non preferred attitude, by repressing the attitude. And once the new influences of it are being repressed, it starts to bottle up in your unconscious shadow side, where the inferior is. Because the ego starts to kinda lose its directive powers over the aux, it starts to mix up with the inferior and starts to gain autonomy, directing the preferred attitude of dom/tert towards negative things, due to tension between the opposites of ego and unconscious mind, by the act of self-regulation of psyche(psyche tries to find a balance to the one sidedness of the ego). If the repression continues, the anxiety grows and can lead to some sort of neurosis, which in jungs model is the cause of unresolved tension between the ego and the unconscious mind.