The Halls of Mandos

[Kuruharan]

I believe Eru's gift was Man's soul was not bound to Arda.

According to the strictest definition in the mythology, that's exactly what death is.

Even Elves died

Only Luthien and Arwen actually died, in the strictest sense of the word. In the Sil it says, "For the Elves die not till the world dies, unless they are slain or waste in grief (and to both these seeming deaths they are subject)...and dying they are gathered to the halls of Mandos in Valinor, whence the may in time return. But the sons of Men die indeed, and leave the world...Death is their fate, the gift of Iluvatar, which as Time wears even the Powers shall envy."

[emphasis mine]