Employee on leave, returns to work, and then quits after working a few days.

While on the leave, the employee was on COBRA and paid the premium for the month in which she returned.

What happens? Since a new qualifying event does the period start over again?

Yes, its a new COBRA event and she must be offered 18 months of COBRA. COBRA doesn't have a minimum amount of time that a person must be covered in order to be eligible for COBRA. Even one day is sufficient.