The defense and security-related sector is legendary for this. I had a friend who worked at a three-letter agency ~20 years ago who saw multiple colleagues quit, get hired by contractor firms and sold back to the agency to work on the exact same projects they had been working on as employees. They got a 2-3x pay bump, and the government paid 3-5x for their services. In one instance, my friend said, a guy clocked out on a Friday and came back to his exact same desk on Monday, with a new "employer" and a higher salary.
Who actually pays for what and how is so mangled that if you want to reallocate someone to another project (or even just pay them out of a different pool of funds!) often the easiest approach is to rehire them through a contractor, or a different contractor.
This is especially useful when projects are wound down. Let's say you've contracted to an org for support or management on a project that you want to kill, you've already obligated some amount of funds, and you don't really want to make that organization angry by ripping millions away from them (the pool of contractors is not large). What to do? Well, you could take Joe and give him a raise by suggesting he work for the contractor instead of you directly. Money's already spent, anyways. So you save your own money that you can use for your pet projects or whatever, Joe gets a raise, the contractor doesn't get a termination that pisses everyone off. Everyone happy, right? Smh.
Per a friend, they are told to use more contractors in the government. Its also not clear if the contractor is actually making more money. Government benefits are significantly better than most contractors will give (I will be all of them).