Yes, sorry, common mistake for non-native speakers. I’ll add a remark to my post.
Yes. The line that tando quotes basically says “born overseas to an ROC citizen who has had household registration.” The important part is having a household (now or in the past) in Taiwan. The fact that HHRs “deactivate” is just, for lack of better words, a bureaucratic thing.
From recent memory, I think @multipass situation should be similar to yours, who has received his TARC through his deceased ROC parent (and is over 20); @paperclip’s application was also based on her deceased parent’s HHR, though she was younger than 20. I think for all of their applications (but you can ask them and make sure), since they were born overseas after some time, their ROC parent’s HHR has already expired.
A household registration is completely cancelled if and only if the citizen gives up his ROC nationality (as far as I’m aware). But this doesn’t invalidate any claims of yours that are based on having an HHR in the past, which your father also fulfills, and which satisfies the requirement that tando pointed out.
For a little bit more insight into the reason why AF384 exists: This criteria was added especially because of applicants who are ROC nationals by birthright, but “who do not have a linear relative in Taiwan anymore.” I mentioned this in my post here Reasons for NWOHR getting TARC - #45 by Lain, at the end, referring to the 2nd link (it is in Chinese though).
Did your father leave any documents behind next to his passport? The more you have the easier it will be once you collect everything for your application, and we could probably give you some kind of assurance that your case mirrors some we had in the past.