[color=#FF4080]I wonder, what would happen if I stay in Taiwan for a long time after my visa expires?
For example, in case if I’m not able to go back to my country because of money problems?
Of course, I’m not thinking to do it 
I just wonder, if I would need to go to jail, or would
I be deported? And if so, who would pay for the ticket, if I do not have any money?.. 
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At worst you get detained (jailed) and can remain in jail for years if your home country govt will not pay for your airfare home !!! And you will be banned from returning to Taiwan for a number of years.
At best, you will be asked to leave by a certain date (very fast) and then banned from returning to TAiwan for a number of years.
Its not a good thing no matter how you look at it. So dont over stay.
In another thread you mentioned marrying your boyfriend in Taiwan? If he is a Taiwanese citizen that will solve your visa problems. Will have to go thru all the hoops of getting your visa by marriage and all that. But he should be able to help you with that.
If caught (which will happen when you try to leave this island, and possibly before that), you will be fined, booted out and blacklisted for a set period of time.
Overstaying a visa is not the way to go. If ever you do decide to return to Taiwan, it’ll cause you no end of bureaucratic problems.