if I could stay later when there’s broken things in prod

In general, or on this instance?

Do you have team retrospectives? That's where I would bring it up in my team. Raise my concerns, explore and understand what team consensus is around this topic, around risks, quality, etc.

If the team consensus and/or management consensus is YOLO - then I try to protect myself from personal investment and going beyond contractual obligations. Because I already know what will come and how it will negatively affect me personally.

It's possible a honest discussion with management about goals and risks could lead to clarified guidelines, requirements, and goals. If it doesn't, I'd probably be looking for a better job/environment. Because I'll be miserable if colleagues YOLO, no matter how careful I am personally.