How loop gain is related to complete transfer function?
Consider a G of 1,000,000,000 at 500 degrees, at 100Hz. (actually the frequency does not matter).
Implement an H of 10 (or 100, or 1,000)
This will be stable, despite the huge phase shift. Why?
Running the math on this, we find

The Numerator, of course, is 1,000,000,000 at 500 degrees phase shift

The Denominator, of course (1 + G * H) = (1 + 1,000,000,000/_ 500 * 0.1)
which becomes 100,000,001 /_ 500


and the combined transfer function is stable, because the phaseshifts cancel.
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Notice the mag/phase is nowhere near the Nyquist point.