I think you need to provide more context about your situation?
I believe they can be strict yeah - I saw some guy writing on Facebook yesterday that his work-based ARC had expired and he’d overstayed by thirty-something days, so he now needs to leave Taiwan despite having a job and life here. I think over 30 days is where it becomes a big problem (don’t take my word for it), but you’d probably want to deal with it sooner rather than later.
No ARC, No visa, then you have no legal right to be in the country. They can be as strict as whatever mood they are in, as its you who is in the wrong. all it takes is one grumpy cop on a traffic stop.