I can't imagine that Kabam will make people miss rewards just because they weren't able to claim them quickly enough on short notice. Even if they are unavailable right now, I reckon that there'll be a fix down the road.
Every event has a function where if the event finishes before you claim all the rewards they go to your stash, this didn’t work as intended for this realm event. Basically this was a bug therefore kabam have to send the rewards
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I don't expect them to send it via mail, but players will be able to claim once they fix it.