There is pretty much always someone willing to buy or sell a stock at some price. The best way to think of the exchanges are as a perpetual auction. There is a line of buyers willing to buy shares at all different prices, and similarly there is a line of sellers willing to sell at various prices. Anyone can 'join the line' by entering a limit order at some price.

Buying at market price simply means you immediately buy from the seller offering the lowest price.

It's very rare for an order book to be empty for a particular stock, but you typically do see the bid/ask spread increase as a stock loses popularity.