Yes, e.g. hardware of hosts breaking, datacenters getting disconnected, etc.

I'm not a solo founder, but if I would be I would most likely pick a solution where I would have to maintain the least amount of infrastructure (e.g. using SAAS/FAAS offerings). That would mean in most cases someone else gets paged if things break. Still doesn't guarantee 100% availability since it can't prevent code bugs from doing bad things, but there would be still less things to worry about.

My team from Founders Cafe told me to create a strategy, kind of like a flowchart of what to do in case I'm not on call when there is a problem. I give them to my employees/freelancers. As soon as I am available, I'll check the conditions of the workplace first thing in the morning.

This is my take. I build products that have the critical infrastructure be fairly simple and hosted completely on third party systems. The most custom part of my system is just the customer portal, which can go down without impacting the core product functionality.

I don't worry about random things.