None of the contractors will be paid, as I understand it, only permanent federal employees.
1) Employees forced to work. Promised backpay by a resolution that was passed.
2) Employees not allowed to work. Promised backpay by a resolution. "Free vacation"
3) Contractors not allowed to work. Will not get backpay, money lost is "gone" forever.
Work for free or you won't have a job around when we get authority to pay you again isn't physical coercion.
OTOH, FLSA would guarantee most federal civilian employees some back pay, though not necessarily their full normal pay.
There's no reason Congress couldn't include back pay under some formula for contractors or employees of contracting firms who lost money due to the shutdown, but historically they have not done so (but, again, this is already the longest-ever shutdown and it may be so by much moreso than it already is, so it wouldn't be entirely inconceivable for Congress to decide extraordinary measures were warranted to address it's impacts.)
Conversely, Congress is not obligated to issue full back pay to furloughed federal employees, though it has in past shutdowns; it may also not be required to do so for those forced to work during the shutdown (though, again, it always has); though because FLSA applies to most federal employees those covered employees are definitely entitled to at least federal minimum wage for the time they were ordered to work. While it seems less likely, the extreme length of the shutdown could lead a particularly stingy Congress to decide back pay beyond what is minimally required is unaffordable.
(Obviously no job is guaranteed, but most Americans still only have enough cushion for a couple months.)
The knock-on effects of this shutdown are going to be around for years.
I predict the knock-on effects of this shutdown will be gone and forgotten within a fiscal quarter.
The best evidence of this is looking at the stock market since the partial shutdown began.