Mortals in the Undying Lands?

[Elthir]

'As for Frodo or other mortals, they could only dwell in Aman for a limited time -- whether brief or long. The Valar had neither the power nor the right to confer 'immortality' upon them. Their sojourn was a 'purgatory', but one of peace and healing and they would eventually pass away (die at their own desire and of free will) to destinations of which the Elves knew nothing.'

JRRT 1971 Letters

Tolkien would be well aware, of course, that Frodo wore the one.