As you say, it's the total market cap that matters in how much value a share is actually worth. But there is a floor to how much an individual share can be sold for before they de-list it entirely, resulting in a lot of volatility for very-low-priced stocks.

When a company on the brink gets a bit of good news, it's easier for it to triple in value than a company with an existing, stable business. Such things can suddenly turn into big, quick wins for the people who were there before the news. (People investing after the news are pretty much just suckers, though market irrationality still lets them sell at a profit to even further suckers.)