my relevant post here
https://www.flyertalk.com/forum/35375667-post111.html
There are 3 relevant time periods here:
1. Before 31 July 2019, "normal" times. If a PRC citizen was living overseas, it was relatively easy to apply for a tourist entry permit to Taiwan (入台证). Here is a representative site:
https://funbirdtravel.com/visa-to-taiwan/. Basically you fill out an online form with work visa/proof of residence and get approved. If the PRC citizen was living in China, I'm not really sure what the procedure is. This info is not easily available on the Taipei Economic and Cultural Office website as they have updated it saying that PRC citizens living overseas can't apply for this anymore.
2. After 31 July 2019 to 27 January 2020. China stopped issuing individual travel permits to Taiwan (from mainland cities). Maybe it still worked if a PRC citizen was living overseas, but I'm unsure.
3. After 27 January 2020. Same as now.