So… you thought you would ask a simple question….
The specifics are in the rules… and I say that because Exodus is a real game changer about this.
Other than Sharon or Baltar, in base game, you only get the cards at start of game and at sleeper phase. If you are executed after sleeper, and are human, then everyone knows it (unless you get handed more cards by revealed cylon!). This is an excellent way to be sure your admiral is Human before new Caprica… hehe.
Sharon “Boomer” Valerii
If Sharon “Boomer” Valerii is selected as a new character,
shuffle one “You Are Not a Cylon” Loyalty Card into the Loyalty
deck. Then, if she was selected after the Sleeper phase, she is
immediately placed in the “Brig” and the player who selected
her draws an additional Loyalty Card.
If Gaius Baltar is selected as a new character before the
Sleeper phase, immediately add one “You Are Not a Cylon”
card to the Loyalty deck, shuffle it, and deal one Loyalty Card
to his player.
Karl Lee and Samual all have notes for execution but not about loyalty cards.
In Exodus, you always have at least 1 extra card in the loyalty card stack. You add a "you are not a cylon" card, mix it up, and the deal a new loyalty card to the new character. So, you could execute a human, and they could get a Cylon card, final five, personal agenda, etc. (the short version of that at least)