The general rule is that if a debt you owe is canceled or forgiven, you must include the canceled amount in your gross income. If the debt is connected to your sole proprietorship business, the income should be reported on Schedule C. The theory behind this is that in most cases you've already received some benefit in exchange for taking on the debt, so in effect, cancelling the debt is equivalent to transferring some type of property to you free of charge.
However, there are a number of exceptions to this rule. One important question to ask is, if you had paid the canceled amount, would the payment (not just the interest) have been deductible? If so, then the canceled debt should not be reported as income.
Similarly, if you purchase some property for use in your business, and the seller reduces the price after the sale but before you pay for it, cash-method taxpayers don't need to report the reduction as income. Instead, it's simply a price adjustment similar to a discount, and you would record the new lower price as the cost of the property.
Another exception applies to debts that are canceled in a bankruptcy or because you are insolvent. Generally, such debt forgiveness is not recognized as income to you, perhaps out of recognition that if you can't pay your debts, the government is unlikely to be able to collect any additional taxes from you!
There is also a special exception for forgiveness of qualified real estate
business debts, but this gets into rather complicated territory. Consult your
tax advisor if, for example, your lender allowed you to refinance some real
estate for a lower principal amount, and you think you might qualify for relief
under this provision.