Example of how face value affects market value
Face value can act as a starting point for the value of a bond on the secondary bond market. Investors will calculate their potential return off of the face value since that's what the coupon rate is paid from but rarely will they give full face value for a bond unless they expect to be able to resell it yet again for even more.
The face value, though, is a fairly guaranteed payout, so a potential buyer knows exactly how much they can expect to get back from that bond, even if they buy it from a third party. So, let's say that the face value of your bond is $1,000, and you want to sell it for what you paid for it, $800.
A buyer might be willing to take it at $800 since they know they're definitely going to return 20% on the bond, even if it's a zero-coupon bond. The time left to maturity will make a difference, though. A 20% return in a year is a great deal. But a 20% return after 10 years? Not so much.
As a result, you may be forced to sell at a much steeper discount to attract a buyer because of the face value and time left to maturity.