Dead Branch is a relic that gives you a random card every time a card is exhausted. Shivs exhaust when you play them so if you have a Blade Dance or 2 (especially if you can upgrade them) you can generate several random cards every turn. Some of these randomly generated cards might also be 0 cost or will exhaust also when they are played which generates more random cards. Basically a Dead Branch run is where you lean in to playing as many exhaustable cards as you can and just seeing what happens. It's inherently an impossible run to utilise a consistent strategy for because the cards you get every fight are always different. This particular run I was lucky that I picked up a Lizard's Tail relic (revives you to 50% HP when you die) as well as a Fairy in a Bottle (revives you to 30% HP when you die) so even if I happened to draw a useless set of cards via Dead Branch at a crucial turn, I was still somewhat safe from just being insta-killed.