In part simple, and depending on exactly which failure scenario you are trying to protect against, expensive and/or complicated
and none of this has anything to do with OBS, so this isn't really the right forum
From a super simple perspective
1. Main OBS fails - failover to second PC running on same site
1. Main ISP connection fails - failover to second ISP connected to same site
1. Main OBS site is offline (site power outage, all ISP connections severed, etc) - failover to secondary streaming PC at another site
Now, you could have battery backup and a good cellular connection at Site A, and that might suffice? for a limited period of time. A backup generator (or whole house battery) will last longer, but if neighborhood outage, ISP links may fail after a while as well
So, simple in that you lay out each failure scenario (Pay attention to 24hr+ power outages on ISP infrastructure) and then have alternatives to cover each. But at some point, with an extended power outage in a given area, streaming from that area has a high chance of no longer working (depends on ISP / carrier Infrastructure specific area details.. in some places if you have an appropriately sized and installed generator you'd be fine for days. other places you'd be offline long before that with nothing you could do about it ... in general, more modern urban areas like to have longer uptime in extended grid outage than rural areas... but ymmv)
I have no idea what 'paying for a service' means. You have to get content out to livestream. If you don't have power to run livestream, or connectivity, then an outside service does you no good.
Now, do companies have workarounds? Yes, and they can get expensive to research ISP connection details (not consumer level, but those with carrier grade SLAs) and then put in place work-arounds (like long reach laser point-to-point, or dark fiber to telco sub-station with week long+ uptime SLA in power outage situation, etc.