So, if I hold a bunch of Private Equity, and my holdings need a continuity of business loan, would I:

(a) have the holding take out the debt, exposing 100% of my stake

or,

(b) have the holding divest a piece of itself, giving me control of the existing and new entities, then have that piece take out the debt, exposing 0% of my stake?

I imagine any PE firm worth its salt would go with option (b).

Presumably regulators would sometimes try to block such deals, but I cannot imagine that happening during the current administration. (Do the regulators even still work for the US government? I thought they were mostly fired.)

Similarly, I can imagine the banks refusing to lend in scenario (b), but I cannot imagine bank leadership being allowed to make such a decision if the PE firm is politically connected to the current administration.

It sounds like you're effectively describing some fraud scheme.

A smart lender will not issue loans without real collateral. If you create a subsidiary, that subsidiary has to have sufficient collateral and cashflow to secure a loan.