Citizenship with a Taiwanese mom who lost her household registration

Is this case similar to yours?

I think the unusual part of your case is this:

I am definitely not an expert on this topic (I am starting to research it myself), but this part seems unusual to me. If your mother would be able to renew her ID card and her household registration, then that should be enough for you to apply for a TARC. But since she cannot renew her ID card and household registration, you’re in a more complex situation.

The question for me is why your mother cannot renew her ID card and household registration. This seems to imply that your mother only had rights to live in Taiwan because of her relatives’ household registration, but never had rights to live by herself in Taiwan. Am I understanding the situation correctly? That means your mother, while in Taiwan, did not attempt to establish her own independent household registration through a 定居 procedure?

If that is the case, then one possible path (though difficult) could be for your mother now to establish her own residency in Taiwan – meaning, she would apply for a TARC, live 1 year in Taiwan, and establish her own household registration. She probably has rights to do this because her father was Taiwanese. Then, after she establishes her own household registration, she could serve as your lineal relative (with household registration) to “sponsor” your TARC application.

I should again stress that I am a newcomer to this topic myself. I hope others with more experience will add their experience.