Money still owed on loan after foreclosure and house has been sold at a public auction?

And?
If your not in bankruptcy where the excess may be discharged (only after using your other assets to satisfy this and other debts), you will still be liable for the deficit.

You borrowed the money using the house as collateral...you agreed to pay back all of what you owed...if you sold the house or if you forced them to makes no difference. If you made a bad investment, or didn't maintain it well, the lender isn't liable...he only did what you asked him, gave you money. If you, (or they), sold it for more and there was excess, you would have rightfully expected it to have been yours.

And yes, you also owe them all the missed payment, penalties and interest along with the costs of having to foreclose.