The producer is the only person who can cancel a performance. If an outdoor show gets rained out, the producer could move us all indoors to do a reading of the play with stools if they want to give that audience a show of some kind.
In this situation, there should be a policy set by the producer regarding ticket sales - if the box office for a particular performance is only two tickets, I would think a smart producer would cancel the show, thereby saving the pay of any hourly workers such as house manager, board op, wardrobe crew, etc.
Also, AEA usually has to agree to hold actors accountable for things like lateness, or not fulfilling their responsibilities - see "Duties of the Actor" in the LORT book for the kind of thing I'm talking about.