I'm shutting down an S-Corp with no assets or liabilities. The Liabilities consist of loans from shareholders, and their total equals the total of Retained Earnings and Capital Stock. For the final 1120-S Balance Sheet, do I just net the above and enter everything as zero?

“I'm shutting down an S-Corp with no assets or liabilities. The Liabilities consist of loans from shareholders, and their total equals the total of Retained Earnings and Capital Stock. For the final 1120-S Balance Sheet, do I just net the above and enter everything as zero?”---->Correct; you need to file an IRS Form 996 within 30 days of approving dissolution. For tax accounting purposes, you will need to file one last S corporation 1120S tax return, marking the return as final return. The form must be submitted to the same IRS center where the corporation sends its tax returns. You also need to pay off any outstanding debt. If the corporation cannot pay off all of the debt, it must declare bankruptcy., and divide up any remaining assets among the owners. As you said, youhave no assets, sothis si NOT your case. Just for reference, rules dictating dispersal of assets should be in the company bylaws that were drawn up when the corporation was formed. Any physical assets, such as buildings, land and equipment, must be liquidated before dispersing the proceeds. If an asset's FMV exceeds its depreciated basis, you will unfortunately need to show a gain on the distribution of the asset to the shareholder on the final corporate tax return. If you have been operating a California S corporation, for example, you will need to file articles of dissolution with the California Secretary of State's office.)

Thank you so much for such a prompt reply. Now that you mention bankruptcy, the S-Corp did receive a 1099-C for Cancellation of Debt. I was personally liable on the debt, but I've since filed bankruptcy and been relieved. The 1099-C was issued to the S-Corp, but wouldn't it actually have been proper to issue that to me personally? And so does the S-Corp have to declare that as income?

“The 1099-C was issued to the S-Corp, but wouldn't it actually have been proper to issue that to me personally? And so does the S-Corp have to declare that as income?”---->I do not think so; since your debt( as you were personally liable for the debt as you said) has been written off by a creditor then you may receive a 1099-c form from the source. You must claims this amount as income on your taxes on 1040 line 21. because I guess you never paid it back- thus making it income. However if you settle this debt as paid in full with the creditor make sure you ask that they agree to the settled in full arrangement and not send the remainder as a loss to the IRS. If the creditor willingly accepts less than as full payment then yu need to make sure they agree not to report remainder. The creditor can refuse but usually does not.
PS; aslong as the S Corp. was the debtor, then you need to report the cancellation of debt income (COD) on the 1120S.