This is a key point. If the flight is employer-paid, downgrading and pocketing the cash could be a firing offense. It is also an IRS (or other applicable taxing agency) violation if not reported.

Any flight can be downgraded provided there's a least one seat for sale in the economy cabin. It's possible that you might have to pay to downgrade -- the change fee might be charged, and a fare difference may apply -- it's possible that the economy seat is more expensive than the first class seat was.