"Completely stuck, unable to proceed" would require effort, willfully attempting to screw oneself over, and willfully ignoring ways to un-screw oneself. Requirements are pretty simple:
(1) Make your deck effectively unable to win. Easiest thing here would be 30 random pillars. Note that you could still conceivably deck other decks out if the other deck did really really poorly and you won the coin toss, or if the AI nightmared one of their own creatures that you had the quanta to play, or if the AI played a singularity or otherwise killed itself.
(2) Burn all extra electrum via a buy/sell loop in bazaar.
(3) Pretend there isn't an oracle button.
You could circumvent item 3 by achieving items 1 and 2 before completing the quest which enables the oracle, I believe. If ai0/ai1 have no 30 card decks (I have no idea whether or not this is the case), you could actually truly permanently screw yourself (barring AI suicide) by obtaining a 30-pillar deck and 0 electrum before completing the ai0 quest.