what did he do at where? How many days has he overstayed for?
He should go to NIA. If his overstay is within 30 days, he can fix things without leaving Taiwan. If more than 30 days, he should go to any overseas TECO to get his new visa.
For his information
"Overstay
- Overstay within 30 days (30th day excluded) but still enrolled: pay the fine and the application fee for the ARC extension
- Overstay more than 30 days (30th day included) and still enrolled: pay the fine and leave the country in 7 days to apply for a new visa to re-enter Taiwan
- Overstay fine:
- 1-10 days: NTD$2,000
- 11-30 days: NTD$4,000
- 31-60 days: NTD$6,000
- 61-90 days: NTD$8,000
- over 91days: NTD$10,000"
From this site
http://oic.nccu.edu.tw/files/11-1000-164.php?Lang=en
If he applied for the 1yr extension of his ARC at NIA, he has a receipt with a pick-up date of his new ARC on it. If not, he has not applied for the extension, so has overstayed. Since you said he is a master course student, I’m assuming he has an ARC.