The MLB Draft was regulated to 40 rounds beginning in 2012. Before that, teams could pick until they were simply done selecting players, which has made the players that the Atlanta Braves were able to sign and develop as undrafted free agents in that era with unlimited draft picks an even more impressive feat.
One of the more notable players of the last 30 or so years in that impressive scouting and development by the Atlanta Braves was left-handed reliever Paul Assenmacher. While Assenmacher won’t ever be a guy who gets traction from the Veteran’s Committee for the Hall of Fame, he did have an impressive career, considering his starting point.