Quote stolen from google search entry:

"It is possible, in other words, for a mortal to live on in the undying lands like an elf. However, Tolkien indicated in his private letters that Frodo and Sam and the others were not counted as elves, and indeed died, even in the "Undying Lands.""

Holy shit! If I didn't know, can we imagine how many people never knew?

This changes a hell of a lot of shit. There's a whole reddit discussion about how the main reason "Ring-bearer's" were brought to the undying lands was just to bring life back to them, since bearing the ring drained them of the ability to enjoy regular life at any level, including protecting them from repeated trauma like Frodo experiences on March 13th and October 6th due to Shelob's venom and being stabbed by a magical hobo-wraith.

The undying lands were just an upgraded realm where injured people could feel again, for the mortals. They still died there eventually, just after living a lot longer like elves get in the mortal middle earth. This is so thought evoking, it has to be a public announcement.