Taiwan's national ID card is very high-tech. There hasn't been counterfeit ID card cases in recent years.
There are many occasions that require two forms of ID - the national ID card and the Universal Health Care ID card. I haven't heard of cases of counterfeit Universal Health Care ID card, either. These are all linked to computer systems and can be easily verified.
There are however, some fake work permit paper out there. There were illegal workers found and were deported.
Do NOT attempt to get fake ID card in Taiwan. You'd be reported and deported.
If you get any fake Taiwan ID, you will be caught. All Taiwan ID is authenticated, I work in the bank and I know because we have a software to test if ID is authenticate or fake. So, having a fake ID will just get you more trouble.