It could be the case that nothing is actually broken. I have unfortunately received a number of similar calls on systems that were working exactly as specified. Random nonsense "disasters" can happen a lot in dysfunctional companies.

I would never in a million years, as a developer, give my personal phone number to a client. That's probably why.

I get the same issue where I work. The client states that "everything is broken," but it often turns out that their own servers are down (or sometimes our API guys made a breaking change and I wasn't informed, but that's not common anymore). I find this stuff out when I get to work in the morning, because they certainly aren't calling me directly.

It's actually the opposite way around for me, but I fill a senior role that intersects directly with high-value vendors. I'm basically on-call 24/7 and I am in the office whenever I feel like it or when I need to work on code.

I log my interactions with my supervisor, he will occasionally check with me to follow up but I can fix 99% of what they call me about on my own. If I need help, it's usually just expert knowledge that I can ask around the office for.

But of course other devs have different roles and workflows.

You're assuming 1) there's a legitimate technical problem and 2) the person calling is management and not a user