This summary is not the rule. The rule text controls.
If you file a lawsuit on time but it gets thrown out for a reason that has nothing to do with the actual facts of your case, you still have a chance to refile. This might happen if your case got dismissed because of a technical or procedural issue, like filing in the wrong court, rather than because a judge or jury decided you were wrong on the merits.
In that situation, this rule gives you six months from the date your case failed to file a new lawsuit, even if the original deadline (the statute of limitations) has already passed. This gives you a second chance instead of losing your right to sue completely because of a technicality.
If you pass away before you can refile, this right doesn't disappear. Your representative, such as the executor of your estate, can file the new lawsuit on your behalf within that same six month window, as long as your claim is the kind that can legally continue after your death.