Rule of thumb in board gaming in general: out-of-turn actions are explicitly mentioned. Just like the rules don't state that you cannot steal money from your competitors.
According to rulebook : "If at any time during the Action phase you want to stop having a card in front of you, you may discard it"
I assume that I can discard a card out of my turn. Is this correct?
So if there is "Live fast, die young" showing as live goal, A and B race discarding the card for being the first one to die.
Who got the live goal?