I have remaining depreciation write-off for properties that I sold last year. Can I continue to use the deduction even though I no longer own the properties?

No. You cannot continue to depreciate an asset that you no longer own.

Did you indicate the sale of those assets on last year's tax return? If done correctly, indicating that an asset is sold will (1) correctly report any gain or loss on the sale of the asset, (2) adjust the then-current year depreciation for the partial year of disposition, and (3) remove the asset from the file, so that it is not transferred forward to succeeding years.

You may wish to consider amending lat year's tax return if the assets were not properly disposed of for tax purposes.