Can I take a deduction for selling a rental property for less than I owed on it?

You can't exactly take a deduction for the sale of a rental property at a loss, but you may be able to take the loss itself.  Please see the following references for a discussion of this situation:

• Selling Rental Real Estate at a Loss
• Is sale of rental property at a loss considered capital or ordinary loss?

Weather you have a gain or a loss on the sale of your rental property has absolutely nothing what-so-ever to do with what you owe on it. It has everything to do with what you "originally" paid for it, along with any property improvements you paid for, as well as the depreciation taken (or required to be taken) on the property.