Here is the article the kind folks at Butler County Historical Society sent me on the Sheriff’s Sale of the land in Slippery Rock, Pennsylvania Joseph Elrod had inherited from his father. He loses his property in a lawsuit from James Clark.
This explains possibly why he was living with Nancy Ralston in 1850 (according to the census) yet he still owned the property. He didn’t lose it until March 1851. Now the trick is to find the court records pertaining to the lawsuit.