When you start a solo challenge with a character that has the same name as a previously deleted character, it will retain the gold of that first character.
I played a bit with a standard char + solo challenge. Deleted that char and created a new HC solo challange char right after deleting the first one, with the same name. Entering the first town, I had +2k gold (which should not be possible after just running through the first zone).
I did not test further possibilities (different char name, etc.), probably some error in the db call or something.