1099 directly for the government
I once had a project with USAID and discovered they used what are called "Personal Services Contractors" quite a bit.
These are basically contractors who work directly for the government as individuals (not as an employee of a government contracting company) and whom the government manages directly.
USAID Personal Services Contractors
They post these on SAM.gov just like any other contract opportunity.
Now, it looks like they peg your rate to something close to the GS schedule and you still have to buy your own health insurance and stuff like a normal 1099, so I don't think this is the deal of the century.
BUT, it's cool to see that at least one government agency uses individual contractors in addition to larger government contracting firms.
Want the full playbook? Check out Going 1099.