Here is how the Minor League portion works.
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Minor league teams can also participate in the draft. AAA teams can draft any player eligible from AA for $12,000, and AA teams can draft any players that are eligible from Class A for $4,000. Players chosen in the minor league part of the draft do not need to return to the original teams for any reason.
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http://www.baseball-reference.com/bullpen/Rule_V_Draft