The scenario would take place after the trade deadline most likely do to one of the participating teams being eliminated from contention or an injury occurring to a team still in the playoffs and them becoming desperate.
Obviously its not exactly the same as working out an extension that wasn't my point, my point was that players are sometimes involved in choosing/agreeing to a trade partner, for example Robert Quinn was allowed to make visits to the Saints and Cowboys, while still a member of the Dolphins to choose the team he preferred.
They don't receive nothing, its a player for a player swap, I release player A with a verbal agreement that he will immediately sign with you, you release player B with the understanding he immediately signs with me, bam we just made a trade after the trade deadline.