Reply to "Drafted but doesn't sign?"

Just to clarify for my own knowledge. My son went undrafted last year, but was offered a Free Agent contract. Would that option not also exist for a player that was drafted, but did not sign by the deadline? Isn't the process over, thereby allowing a player the freedom to go to MLB tryouts, or sign later, before the next draft?

I am not passing judgement on the idea, just seeking clarity on the rules.
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