The phrase "sink or swim" applies to essentially every coach, whether in a winning or growing situation, with an organization that will support their every move until failure becomes noticeable. This does not strictly mean losing in the regular season or getting bounced in the first round, as behind-the-scenes issues can cause a genius mind like Mike Malone to be let go.
One of the only coaches in the NBA who receives a pass is Steve Kerr of the Golden State Warriors. His team could face any outcome, and his job will still be safe, because he has produced championships.