Take an ROC-born, naturalized American citizen who hasn't lived in Taiwan for 30+ years. She hasn't renounced ROC citizenship but, by not maintaining household registration, IIUC she no longer has a right of abode in Taiwan. How easy would it be for her to get a permanent residency in Taiwan? What about for her (non-ROC-national) family members?
Taiwan's citizenship won't be gone without formal renouncement. It's possible to lose Taiwan citizenship involuntary if the citizen acquires mainland China's(PRC) citizenship. Taiwan's current law does allow dual citizenship unless the citizen works for Taiwan's government. She can restore the status pretty easily as long as she has the appropriate documents.