I assume here you mean that she “suspended” her NHI, which is no longer allowed.
But as you said, there still seems to be a way of “unenrolling” from NHI, by “terminating” HHR.
I am trying to understand what this means to “unenroll” from NHI by “terminating” your HHR. Is it the same as getting “moved out” from HHR after 2 years abroad, but without needing to wait 2 years? If you could say to the HHR office, “I am moving out of Taiwan next week for several years. Terminate, i.e. move out, my HHR as of my flight date.”, then would that immediately remove your NHI payment obligation, as long as you continue to stay out of Taiwan?