My Co-worker was in Taiwan for well over 183 days in a Taiwan tax year but continued to pay taxes in his home country (the UK) and never filed taxes in Taiwan despite him now being a tax resident. Now he has claimed his taxes back from the UK as he didn’t qulaify being a tax resident in the UK so effectively paid no tax for a year. Is it possible Taiwan can track this down and demand the taxes be paid. He was only ever in Taiwan on visa exempt business travel so never had a residence card.
Nothing will happen unless he does apply for residency someday (of course he should file). Should he become a resident, when he files the first time they’ll ask why he didn’t file for this current period (tax office can see all of his entry/exits at this point).
Generally, Taiwan is not that strict in enforcing tax-rules. Many landlords get away with not paying their taxes.
I am more surprised your colleague was easily able to reclaim the taxes back from the UK - from what I have heard the authorities there usually don’t let people escape UK taxation that easily (especially if they don’t have proof that they filed and paid taxes somewhere else).