I recently made a visa run to Hong Kong after overstay on an ARC. The Hong Kong visa run guide and this thread were a huge help to me, so I thought I would leave my notes to help anyone else in a similar situation.
I overstayed 11 days on my ARC from a one-year contract with Hess (awful experience, by the way.) I thought my good looks and my winning powers of persuasion would see me through to some sort of extension at the ARC office, but no dice there. Maybe this goes without saying and I’m an idiot for assuming otherwise, but the last day on your ARC is the LAST DAY you may remain in the country. If you are in Taiwan on the day after that, you are overstaying. Ten days of overstay means an NT$2,000 fine at the airport. Eleven days (up to 20) means NT$4,000. A SINGLE DAY OF OVERSTAY COSTS YOU YOUR VISA EXEMPT PRIVILEGES FOR ONE YEAR. Live and learn. I think ARC extensions are possible, but that is another topic entirely.
I used the Hong Kong visa run guide to help me find the TECOS office. I took the Airport Express Line from the airport to Hong Kong station. Then I changed to the Island Line and rode it one stop to Admiralty Station. Lippo Center isn’t far, and it is pretty hard to miss. It’s a small skyscraper with “LIPPO” across the top in huge letters. Look for the Ruth Chris Steakhouse and you’re almost there.
At the TECOS office, you take a ticket and wait. I arrived at around noon and took a number. According to the web site, 11 a.m, is the cutoff time for getting your visa application submitted if you want to be eligible for rush processing and get your visa the same day. Submit after 11 a.m. and you will not get your visa until the next day, the web site says. However, my number wasn’t called until almost 2 p.m. and I had to run get new passport photos, since apparently mine were the wrong size. It was 3 p.m. by the time I had everything submitted and the agent asked me on the spot if I wanted a visa today. Um, yes? I returned at 4:40 p.m. and picked up my new visa. You leave your passport with them and they put it on a blank page.
The documents I submitted to the TECOS office are as follows. Some of these might be unnecessary, but this is what worked for me:
Copy of the ID page of my passport
Copy of my bank book showing that I had a balance of NT$40,000
Copy of my cancel contract agreement from my last employer
Copy of the receipt from the airport immigration office showing that I paid the overstay fine
Printed copy of the online visa application from the TECOS web site (you need to go on the web site, fill out and submit a copy electronically during business hours AND bring a printed copy with you)
2 passport photos (there’s a mall above Admiralty Station, and there is a Kodak kiosk in the mall where you can have passport photos taken and processed on the fly)
Copy of my e-ticket departing Taiwan 55 or so days into my 60-day visitor visa stay
Apology/explanation letter
The explanation letter is your chance to have some fun with fiction. You need to offer up an explanation for your overstay on your last visa and promise from the bottom of your little heart not to do it again. You are asked to write it at the office. Mine went something like this:
Dear Sir or Ma’am:
Please accept my sincere apology for overstaying my resident visa/ARC. I admit that I overstayed and it was my fault that I did.
The reason I overstayed was that I was told by a coworker there was a 14-day grace period after the expiration date of my visa during which I could leave the country. After I contacted the NIA, I found out that this information was incorrect.
I left the country as soon as I realized I had overstayed my visa.
Sincerely,
(Your name)
A few afterthoughts:
I was waiting in the TECOS office at 1 p.m., when an agent came by and placed a cover on the automated ticket machine. So, after 1 p.m. it was impossible to even print out a ticket. I don’t know why they seemed to be bending the rules for same-day visa applications that day. Maybe they had a slow day and figured they could maximize revenue collection that day by offering everyone same-day service, which does cost a bit more. I can’t say for sure. One thing I can say is that after 1 p.m., no one was getting a ticket and it was therefore impossible to start the application process. If you arrive at the office after 1 p.m., you’ll have to start looking for a hotel. It’s probably best to get there as early as possible (the office opens at 9 a.m.) if you are hoping to get a same-day visa.
I submitted my electronic copy of my visa application five days before I went to the visa office. This was OK, apparently. Outside of business hours the system won’t accept new applications, though. Business hours for the TECOS office are 9-5.
I made my run on Dec. 23, 2013. The ticket to Hong Kong on short notice cost NT$6,026. A ticket back from Hong Kong was a bit less, about NT$5,300 after conversion. A departing ticket from Taipei to Manilla scheduled for the end of my visitor visa was NT$2,150. On my way out of Hong Kong, a ticket clerk for China Airlines asked to see my departing ticket from Taiwan in 60 days or less, and I did get the feeling that they would have forced me to buy one in order to get on the plane back to Taipei. A visitor visa cost me HK$1,280 plus a rush processing fee of HK$200 for a total of HK$1,480. At a conversion rate of NT$3.88 to HK$1, a new visa with rush will cost about NT$5,748.40. Don’t forget to get that converted to HK dollars, because the office does not accept NT$. Add in a few extra small expenses like lunch and MTR fare, and god forbid you have to stay overnight, a hotel room, and you’ll have the total cost of a visa run. I didn’t total it up because seeing how much money this cost would make me want to kick myself in the groin all over again.
Here is the TECOS web site: tecos.org.hk
The visa application form can be found on this page: tecos.org.hk/basic-documents … pplication
There is a travel agent in the mall above Admiralty Station, too, if you want to zip over with your new visa and book a ticket back to Taipei.
Also, if you’ve never been to Hong Kong before, get a load of the ten dollar bill. It’s like My Little Pony and the Care Bears got together and decided to mint currency. 
Last, a sincere thank you to everyone who posted about this. I would have been very much in the dark without the Hong Kong visa run guide and this thread. Thank you, thank you.