When a team designates a player for assignment, he is removed from that club’s 40-man roster. The team then has a period of time with some ability to impact what is next for that player. This is colloquially referred to as “DFA limbo”.
The team can trade the player to another club, unless the trade deadline has passed and the new offseason has not yet begun. The team can also place the player on outright or release waivers. This limbo period can last as long as seven days. The waiver process takes 48 hours, so the team has a maximum of five days to work out a trade.