Claim unused portion? There's no such "claiming" unused depreciation.
Many folks don't understand that depreciation is not a permanent deduction. When you sell the property, all depreciation already taken on the property is recaptured by the seller in the year of the sale. That recaptured depreciation is added to your AGI and is taxed at the ordinary income tax rate. So there is no such thing as "deducting remaining depreication". But there is a "recapture" of depreciation already taken. Another aspect of the recaptured depreciation, is that it also has the potential to bump you into the next higher tax bracket. But there's a limit for recaptured depreciation. It gets taxed anywhere from 0% to a maximum of 25%
