You CAN go to the tax office yourself with a friend to find out the situation. Really, you need to be doing the math yourself about how much you’re paid and how much you’re owed. You can’t know about the tax if they aren’t giving you monthly receipts for taxes paid.
Chances are great that they are NOT paying your taxes, or are not paying them for your entire salary–they’re under-reporting the amount you’re paid. If this is the case, you could be asked to pay the difference! Yes, you can aske the tax office to ask your employer to pay the difference, but if the tax office finds out that they are deliberatly under-reporting your salary (can you prove this? If you’re simply paid with an envelope, there should be an amount written on the envelope and they should have a second book that you sign when you accept this cash, right? You may have to be able to copy that–a very closely guarded illegal book) the school will be fined. I don’t know how much, but I think it’s quite a lot. What they are guilty is tax evasion.
All this is to say, if you’re planning to leave your JOB in a couple months and get another job in Taiwan, it might be a good idea to straighten this thing out. If you’re leaveing TAIWAN, maybe it isn’t worth it. Chances aren’t that great that you’ll actually get to collect your tax rebate anyway, and you could end up having to pay what the school has not.