The obvious answer would be that slavery ended in 1865 after the passage of the 13th amendment I suppose. However I imagine there were a few isolated slave owners who willingly or ignorantly (assuming even they didn't know about the passage of the amendment) carried out slavery on their land after slavery was illegal. Is there any record of the 'last slave' to be emancipated?
I actually posted a related answer last month:
Levine mentions incidents in Texas and Georgia, including one master who explained it by saying Lincoln's death had restored slavery. One African Methodist Episcopal missionary in Georgia said, even four months after Appomattox, "The people do not really know that they are free." This did eventually fail, one plantation at a time, without much fanfare. Levine quotes one newly-freed girl saying "We stayed [on the plantation] another year after freedom" until "we finally found out we were free and left." Sadly, though Levine doesn't speculate, it's unlikely she was the last to learn.