I don't see why the Valar could not in that circumstance have indefinitely halted the aging and metabolic processes for the Númenóreans. Morgoth did it to Húrin when the latter was prisoner in Angband, basically keeping him in what looks like a state of mental awareness with physical stasis.
The other option is that their bodies did die, but their spirits were prevented from leaving the cave and going on to whatever awaited Men after, until they'd been specially judged.
Of the two, I think the former is more likely.
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Music alone proves the existence of God.
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