The mortgage or lien can and should be paid off prior to the bargain sale or with the sale proceeds received by the previous owner. This produces the best tax benefit to the donor/seller. If the charity assumes the lien or mortgage, then this is considered taxable income to the donor/seller.
Assuming there are net sale proceeds to the donor/seller, these proceeds can be used to establish a charitable gift annuity. Or the gift portion of the bargain sale can be used for a gift annuity contract. For example, a donor arranges a bargain sale of real estate with The American College of Financial Services for the sale price of $100,000. The property has an appraised market value of $200,000 thus making this arrangement a bargain sale of $100,000 and a charitable gift of $100,000. The donor can turn around and donate the sale proceeds ($100,000) received in this deal for a charitable gift annuity. This produces the maximum tax benefits for the donor. On the other hand, the charity can agree to a charitable gift annuity contract based on the donated portion ($100,000) of the bargain sale.