"is this a US thing or can people do that here?"
The UK process of "Administration" is similar, if not exactly the same. The court gives the company protection from its creditors, but in exchange, the company is administered by a court-appointed officer to ensure that the promised restructuring is actually carried out. The US system (like the Irish company law process of "Examinership") operates will less direct supervision from the courts, and allows the company more leeway, but the intent is the same: protection from bankruptcy while the company attempts to restructure.
Unfortunately, most people in the UK think that "gone into administration" is exactly the same thing as "gone into bankruptcy", so it tends to hasten the demise of companies as orders dry up. (cf. the similar failure to understand the difference between "laid off" versus "made redundant").