Hmmm. My Libertarian friends usually mean “Democrats who were left behind by the Democrat Party’s leftward march and thus became “new conservatives” aka “neo-cons.””
The short version is “FDR/Truman/LBJ type” Democrats or maybe “Pre-McGovern” Democrats.
I'm not sure why former Democrats who saw the light and became conservatives would need their own special sub-category... considering that many (if not most) of us were liberal Democrats when we were young.