The employee does not have to terminate for COBRA to apply. COBRA applies any time the employee loses coverage, for any reason except gross misconduct. This includes reduction in hours, loss of coverage due to a leave of absence (excepting FMLA), or any other time the employee became ineligible for coverage under the plan's rules.
There are two possibilities here, and whether the employee is or is not currently employed does not matter to either of them:
1.) The employer left the employee's coverage in place during an LOA, as you suggest, and is now charging back the employee. That's fine; IF the employee was notified of this in advance and given an option of how to pay - weekly/monthly during the leave, all at once up front, after the leave, etc. If they didn't, it's questionable whether they can charge the employee now. The employer might win if it came down to it, but I'm not laying money either way.
2.) The employer covered the employee in error after coverage would normally have expired (once FMLA expired the employer had no legal obligation to continue coverage, and many employers will require COBRA after 90 days, which is slightly more than FMLA), and is now trying to recoup. Sorry, but they don't get to do that.
And taking the payments out of accrued vacation might be okay in some states, but definitely NOT in either MA or NH, with the single caveat in NH already mentioned. And I very much doubt that is the case.