If you choose to _sell_ at $1 you will likely get a warning because it will fill instantly at the current market rate despite being a limit order. However you can choose to buy at $1 and there's no reason for it not to be accepted into the order book. In fact you often see this via Nasdaq TotalView during low liquitiy events such as right as the premarket opens where someone is bidding $1 or $0.01 for shares of a blue chip company.
Market makers, which are required to maintain a quote, have been known to put in a bid at $1, knowing it will never actually execute. Until the price drops below a dollar, which it turns out does occasionally happen. Oops.
The same applies in reverse.