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Lester Hudson played under two 10 day contracts with the Cavs and finished the second one today (4/19).

He is going to sign with the Memphis Grizzlies. Will he be eligible for their playoff roster?

He is eligible. The deadline is only for players waived, and since he played out his contract fully, for all intents and purposes Lester Hudson is the same as someone like Shaq who wasn't on any rosters, free to join any team and be eligible.