I have been responsible for mission critical systems for years. It is much easier now that we are able to work remotely, so people do not need to be in the office to do most of work. But back in the days when it was necessary to have a skeleton crew in case of emergency, I used to ask staff to take turns so people who had families far away could travel home. Most people were quite cooperative.
I worked for a very religious Jewish man for 15+ years. I attended meetings and worked on Fri and Sat on his behalf. He often told people to call me if he was not available. He let me make many decisions on my own. As a 20/30 something, it was a lot of responsibility, but I also learned a lot. I used to make fun of him that was the only reason he hired me.