former history major
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The non-waiver trade deadline is July 31 @ 4 pm EST. After that time, teams can still make trades, but the players involved must clear waivers. Throughout the month of August, players will be placed to the waiver wire. If no team claims them, they are free to be traded. For example, if the Yankees are interested in trading Sheffield away, they will place him on waivers. If no team claims him, they can trade him to anyone.
If a team claims him, the team that currently has him on contract can release him and the team that claims him is responsible for picking up the contract. This happened a few years ago when a reliever (can't remember who) was making $4 million and the team placed him on waivers--they were trying to trade him to a playoff contending team. One of the rivals of the Po-C teams claimed him to "block" the trade. The team cut him and the team that claimed him was stuck.