Strike-Out-Not-Out

Sometimes, you can see batters swing and miss after two strikes, but runs to first base. As everybody knows, swinging and missing after two strikes is strike out because swinging counts as strike. However, there are special occasions when batters are allowed to go to first base to get safe. When batter swings and misses and catcher also misses and doesn't catch the ball, batter can attempt to run to first base while catcher runs to get baseball and throw it to first base. If batter touches the first base before any fielder catch the ball, the batter is safe. The batter is out if the ball reaches the first base first.
If batter is safe in first base, batter becomes a runner, but out count number doesn't go up. However, if the batter gets out, one out count is added.
After two outs, batter can run after getting strike out not out, regardless of having runner on 1st base or not. However, if the out count is zero or 1 and there is runner on 1st base, strike out not out doesn't work.
http://mlbkorea.com/sub_hotclip.aspx?id=3311