Before the Draft, I clicked that on the trade block box on my best offensive lineman thinking that I could not afford him. Well, another team tried to inact a trade for that player and it looks like it almost went through without me even accepting the proposal, but was blocked thank God.

So my question is, if you click that box on any player, can another team just offer you a trade and have it go through without us accepting it?

Not that I know of. That just lets other GM's know that player is eligible for trade.