It makes sense, especially if Erase is literally Erasure - taking with it every last trace of existence that person had.
This oddly ties in with my theory about why Xion was forgotten in KH2 XD if we say her outer appearance is made from Memories of Sora/Roxas, than that is what everyone's Memories of her will be linked to. Once those returned to their proper place, however, the thing everyone's Memories were linked to as far as Xion is concerned disappeared - making the Chains of Memories between them delink and fall apart.
That is not to say Xion disappeared completely - the Core that lies underneath the Memories still exists possibly, but the concept remains.
Xion as we know her was "Erased".
Gotta love KH equivalent of suicide XD
heres my idea on xions existence
soras heart released = roxas
kairis heart lost = namine
kairis and soras heart being released at the exact same intant = thus created xion from both soras and kairis memories.
this would explain why she resembles kairi and has a special connection with sora
as for the term errased i agree with suffering angel KH equivalent of suicide