Now correct me if I'm wrong as a mere Canadian and not 100% sure but if he dies doesn't that mean the (D) KY governor gets to appointment a replacement for what would have been his remaining term? Not wishing his death, obviously, just wondering what happens in that event?
For senator, most states allow the governor to appoint a replacement until a special election is held. In 5 states, there is no appointment and a special election will be held immediately.
For representative there is no appointment, the US constitution requires a special election.
I believe that the appointment can be anyone, traditionally it's someone from the same party. I seem to remember in one case the wife of the senator was appointed, his term was almost up and she knew what his position would be so it made sense at the time.