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The corporation will report that loss on its Form 1120S. However, it can only report the amount of the loss that is "at risk". This calculation can be complex but sometimes is relatively simple. Basically, to the extent that your S corp has invested cash or has recourse debt, it will be at risk and that will be the amount that is available for deductible loss.
Yes, that would be debt for which the corporation has liability. If, due to the terms of the debt or due to the terms of the LLC agreement, the corporation is protected from liability under a debt, then it is non-recourse and will not be counted as "at risk". If however, the members of the LLC have responsiblity for the debt, then it is recourse and will be a part of the at risk calculation. For example, if the members invested $10,000 each and then the LLC borrowed $300,000, your at risk amount would be $10,000 (amount invested) plus whatever portion of the $300,000 that the corporation is liable for.
Once this calculation is made with respect to the LLC investment, you will have to do a similar calculation at the shareholder/S corp level. If the LLC loss creates a net loss at the S corp level, you would have to be "at risk" at the shareholder level to be able to deduct that loss on your personal return.