Baseball, by the Rules

Pitcher Drew Rasmussen, of the Tampa Bay Rays, ducks to get out of the way of a throw from catcher Danny Jansen, who is attempting to throw out a base stealer at second. Meanwhile, batter Johnathan India, of the Kansas City Royals, recovers from swinging through the pitch.
The Pitch is a Strike...
The pitcher pitches, and a runner on base takes a shot at a stolen base. The pitch itself results in either a called strike1, or a swinging strike, though in this case, it does not result in a strikeout. Now, it's time to chase down the base runner.
The strategy for defending against a stolen base depends very much on the situation; how many runners are on, which bases are under seige, those sorts of things. Ultimately, it comes down to the catcher, who may or may not throw down to the base in an attempt to get the would-be-thief out. Making a throw comes with risks; if the catcher isn't accurate, things can get dicey for the defense very quickly.