Most of the last mile fiber network is passive (doesn't require active electronics to pass the signal like DOCSIS/cable internet or ADSL).

Cable and DSL typically have the equivalent of UPSs in their neighborhood nodes, but they often go unmaintained.

Your ISP has working battery backups. Don't expect it to stay on for longer, widespread outages though. When the power is out for a week, satellite is usually the only thing that will still work.

ISPs that still provide DSL, really don't want to put any effort into maintaining their equipment these days. They probably stopped replacing the batteries a long time ago.

Welcome to the secret internet when all your neighbors stop hogging it! (Well, less of a thing these days)

I was an early adopter of a cable modem with AT&T before download bandwidth caps. When the neighborhood went dark, I jumped to my computer and beeping UPS to download everything I could to find my max speed.

Your fiber ONT box (where the fiber signal gets converted to copper ethernet) probably has a backup battery in it. This is especially useful if you have VOIP landline phone service through your fiber provider so you can call for help if necessary when the power is out. You or your provider will need to replace this battery every few years, just like with a UPS.

I've smelled the diesel fumes and heard the backup generators near my city's old telephone/internet central during a city blackout a bit over a decade ago, so at least those stay on during blackouts, but you'd think that various boxes along the way to the central might need power, right?