The Unfinished Vault (named Fake Vault 13 in-game) is a small cave with some construction signs for what was to be a Vault-Tec Vault, but was not finished before the Great War. Its intended number is unknown.
It must be noted that the cave for the fake Vault 13 looks exactly like the cave for the real Vault 13.
One of "Caves" random encounters has the similar layout without construction signs.
The Unfinished Vault appears only in Fallout 2.