In cases where unions are involved, the terms of the furloughs are usually negotiated with the unions beforehand. I don't know about contractors specifically, but for civil servants, their unions were definitely involved in the furlough negotiations during sequestration. In this case I don't know how much they'd get to say since the entire federal government has shut down and the issues go all the way to the highest parts of the government.
Also keep in mind furloughs are not layoffs - just unpaid leave.
Correct. They only do this for government employees not contractors. Contractors don't get paid.
I went through the shutdown back in the 90s as a contractor working at the Whitehouse and we all got sent home without pay. If you had saved up vacation you could use that, otherwise you didn't get paid and there was no back pay for the furlough period. We basically got laid off for that time period, whereas the government employees got a paid vacation.
Also keep in mind furloughs are not layoffs - just unpaid leave.