Recent papers [GK03,HT03] define the weakest failure detector for solving the Non-Blocking Atomic Commit problem (NBAC) in a message passing system where processes can fail by crashing and a majority of processes never crash. In this paper, we generalize the result by presenting the weakest failure detector to solve NBAC in any environment, i.e., without any assumption on the number of processes that can crash. We present the result in a modular manner through determining the weakest failure detector for quittable consensus, a variant of consensus introduced by Hadzilacos and Toueg [HT03].