This summary is not the rule. The rule text controls.
When a case gets dropped or settled before it's finished, the lawyer for the person who started the case (the plaintiff or petitioner) has to tell the court officially. They do this by filing a paper called a "stipulation" or "statement of discontinuance" with the court clerk. This paperwork needs to be filed within 20 days after the case is discontinued.
There's an extra deadline if the case already has a hearing or other court activity scheduled soon. If that scheduled activity falls within those same 20 days, the lawyer must file the discontinuance paperwork before that scheduled date, not after. This makes sure the court and everyone involved knows the case is over before any more time or resources get spent on a hearing that no longer needs to happen.
This rule basically exists to keep court calendars clean and accurate. Without it, courts might waste time preparing for hearings on cases that already ended, and clerks wouldn't have a clear record of which cases are still active.