The closest equivalent to that today, in most white-collar roles at least, is contracting. Usually not a physical walk-on hire anymore, but it is often quite a quick process (sometimes as little as a few hours), from "I need a worker", to "I can do it", to "get cracking sonny". And it's then, days / weeks / months (usually not years) later, a similarly quick process, from "we don't need you anymore" / "I'm outta here", to "don't let the door hit you".

But the contractor usually needs to be "employed by" some agency company, that guarantees his/her suitability, and that handles the (not insignificant) paperwork / legalities, and that takes a handsome cut.