I'm always around. Luckily, being I work in analytics and data science, most of my stuff shuts down after 5PM my time. But, I've always conveyed to my boss that I am around if things break no matter the time or day.
In the past, when I worked in the video game industry, we developed massively multiplayer online games. Hundreds if not thousands of players playing on the same server around the world. While I was not specifically operations, I had to be available around the clock if the service goes down or something breaks where we had to do emergency patches in the AM.
I can't count the amount of times issues struck in the wee hours. We managed this by having the typical on-call schedules and rotated people around in our team to wake up, call the IT guys (or send them cabs at whatever bar they were in that night haha), wake up the programmers (if needed), and then notify the customers that hey, we are up and on the case. Nothing brings me more joy than calling the sys admins at 3AM their time and waking them up.
Besides that, patching or major launches to the game usually meant 24 hours of work. I have slept at my desk and have covered people up with blankets at the office. Believe it or not, it was actually pretty fun for most of us. We really enjoyed being there and the business was really cool with covering us while there.
The wildest story thus far is me pulling like 15 hours and checking out super late. I drove home around 3AM and was pulled by a cop in my city for my tail light being out. I pulled over to the side of the road and turned off my car. The police officer pulled behind me and forgot to put the car in park as she tried to exit. The police car started to roll forward. She tried to get back in the car and was dragged forward slamming right into my car knocking out the other tail light.
Her boss had to come and write up the report while her co-workers poked fun. I never got a ticket and her boss said this was her first night out alone. She was likely nervous.