This has been going on for decades. Infiltration of places of power has been a goal of the New Left since 1969-70 as a means of revolution.
They concentrated on the Education system and have practically total control of it.
I never heard of “headless nails” but in Chicago with the idea of ghost payrollers it sounds similar.
“Headless nails” are different from commie teachers and professors because they stay silent until the war comes.