A government’s exercise of eminent domain is really a condemnation where private property is legally taken for public use. Gain (or loss) from the event is the difference between the award you received and the adjusted basis of the portion of the property taken. If the award is more than your basis, you have a gain which you report as a capital gain unless you are eligible for and opt to apply the home sale exclusion. If the award is less than your basis, you have a loss which is not deductible. Find more information in IRS Publication 544 (https://www.irs.gov/pub/irs-pdf/p544.pdf).
Debt on which a person is not personally liable. In case of nonpayment, the creditor must foreclose on property securing the debt. At-risk rules generally bar losses where there is nonrecourse financing, but an exception applies to certain nonrecourse financing for real estate.