when you sign someone as an amnestied player, you take on the remaining years in their contract - BUT, if you only bid $1M you are only paying $1M per year and the original team pays the rest of the contract, though it's not on their cap.
from what i know, amnestied players can't be traded until after July 1. so they have to play a whole season for their new team.
not clear what happens if they get bought out AGAIN after being claimed on the amnesty wire.
but basically, you have to claim them to play them, not able to claim them as a trade chip. unless you're willing to stash them for a year. which i'm sure someone will do.