My tax client received a final K-1 for an s-corp. On the notes, their accounting firm mentioned that my client had remaining basis both at the federal and state levels. Is this a capital loss or ordinary loss?

it'd be a capital loss absent 1244 treatment ;Section 1244 of the tax code allows losses from the sale of shares of small, domestic corps to be deducted as ordinary losses instead of as capital losses up to a maximum of $50k for individual tax returns or $100k for joint returns. And there are rules under 1244 as they relate to adjusting outside stock basis for pass-thru income, loss, etc. from s-corps. However, losses passed through to the S corp shareholders are limited by the following provisions in the order listed ;The basis limitations of IRC; The at-risk limitations, and The passive activity loss limitation . The amount of a shareholder's stock and debt basis in the S corp is very important. Unlike a C corp, each year a shareholder's stock and/or debt basis of an S corp increases/decreases based upon the S corp's operations

Note;Shareholder's making loans to their S-Corp may take a tax deduction in the current year for losses in excess of their stock basis, but only to the extent they have loan basis I mean adjusted basis in S-Corp debt at the end of the year(ordinary loss reduces your stock basis and balance in your S corp AAA acct. Your S corp keeps track of all its icome/loss in AAA. Your AAA balnce can never be below zero due to regular ditribution ). As long as you, the shareholder, had both an equity investment and advanced a loan to the company, then you must restore your loan basis before restoring your stock basis. When your S corp terminates, unless your distribution exceeds the balance of AAA, you do not need to pay tax on the distribution.
One other "S corporation liquidation" wrinkle should be mentioned: Any assets that your S Corp owns at the time of liquidation will in effect be distributed to you, the shareholder. If an asset's FMV exceeds its depreciated (adjusted)basis, you will unfortunately need to show a gain on the distribution of the asset to you on the final corporate tax return. In other words, if you purchased a $2k laptop computer that you fully depreciated and then you distribute the laptop to yourself as shareholder, you need to book a gain on the distribution. The gain equals the FMV of the laptop. You don't want to distribute assets to shareholder, you, if the assets' depreciated basis exceeds the FMV. For assets carried at a book value in excess of FMV, you want to have the S corp sell the assets to generate the loss. A dissolved corp ceases to legally exist and the effect this has on its shareholders depends on how it was dissolved. If the scorp is dissolved voluntarily and its assets distributed to the shareholders without paying all remaining corporate debts, the shareholders could become liable for the debts. If the corp is dissolved involuntary by the court or administratively by the state, the shareholders can incur additional expenses and liabilities.

This is exactly what was on the K-1 in the footnotes:

The shareholder's ending basis was $22931 for federal and state and $23534 for amt and wi amt.

So, if a capital loss then, where on the tax return should it go?

as this was a final return for the s Corp then balance sheet would have been zeroed out through liquidation and therefore the k-1 should have reflected this to the shareholderYour stock is a capital asset. You will report a capital gain or loss on sch D. If you made the loan with a formal promissory note, the payback counts as capital gains income when you and your fellow owners decide to close your S corp . Otherwise it's ordinary income, which may result in a higher tax rate.