Depends how the company is shutting down. When shutting the company, after the company has fulfilled its obligations(such as servicing its debt, employee salaries), if anything remains, that is distributed back to shareholders.
I don't know the "definition" of face value, but I will try to explain it. When you purchase a share, you are actually putting money into that company. But this investment opportunity is priced at a premium.
Example:
Lets assume Mukesh Ambani wants to take a company "RELIANCE LOGISTICS PVT LTD(RELLOG)" public. He decides that the face value of share is Rs. 10, and there will be premium of Rs. 100. So in the open market, he will be selling you a share at Rs. 110. (face value + premium).
So lets say you are subscribing to 200 shares of RELLOG. So you will be paying 200 x 110 = 22000. Now, out of this Rs. 22, 000, not all is going to RELLOG's account. Only 200 x face value, i.e, 200 x 10 = 2000 is going to RELLOG's account. The rest 20000 you paid was a premium. The better the opportunity for profit, higher is the premium.
I hope you got it.
Now what is the share price is less than face value? If you have understood the above explanation, you can derive that such share have negative premium(screwed up)!