Staying Past ARC Time?

Hello all.

My work with my employer finishes on 2/27/13.
My ARC says its “date of expiry” is 3/14/13.

Some questions…

When my contract with my employer (Hess) ends, does it mean my ARC is immediately terminated, or can I stay until the expiry date on the ARC card?

Can it be extended (by a week or two)? What are the consequences if I stay in the country past the ARC expiry date?

The reason I ask is because I am taking up employment in Japan and need to be in Japan on 3.24.13 or earlier, but want to stay in Taiwan as long as possible because of how expensive Japan is. I do not want to pay for 11 days worth of hotel/hostel stays in Japan + food.

Thoughts? Suggestions? Loopholes?