Baseball, by the Rules
Strikeout During a Stolen Base
When a baserunner attempts to steal during a pitch, and the result of that pitch is a strikeout1, then the first consideration is the number of outs— if the strikeout is also the third out of the inning, then nothing else matters: the inning ends. The stolen base attempt is negated, as if it never happened in the first place2, and the game continues.
If, on the other hand, the strikeout was not the third out of the inning, then play continues, and the defense can attempt to get the runner out. If the defense can nab the runner, this means they will have gotten two outs on the same play; this is called a “double play,” sometimes further labeled a “strike ‘em out, throw ‘em out" double play.