Consider for example the case of a subprime mortgage loan where the borrower cannot afford to make payments and the value of the property is not sufficient to repay the amount of the loan. The mortgage is not worthless, but it is in effect a zero coupon bond. If you estimate the market value of the property at one half of its peak value, one then must deduct legal expenses, and perhaps five years of property taxes, utilities, insurance, maintenance, and management fees. In this, one can arrive at a reasonable estimate of the likely proceeds a lender will receive and the loan's current value.
It is rare that real estate has no value. Most property can be sold at some price. But the price may be so low that expenses will wipeout any residual value to the lender. Still the lender is best off to sell the property if he is willing to wait. His recovery for tax purposes of donating the property to charity is probably less than his expenses. Abandoning the property to avoid paying maintenance and other charges probably will not work, and would be expected to result in deterioration of the community.
Rather than taking this loss to sell the loan, many holders of toxic paper decide to hold the loan until real estate prices can be sold and/or the property can be sold. But this ties up their capital and reduces their ability to participate in their usual financial activities. This is the essence of the subprime mortgage debacle.