Which is where the backup battery comes in play... Mains can be assumed present until there is a fire, upon which the backup battery takes over. This is in fact EXACTLY how those EXIT signs work: they are on all the time, trickle charging a battery, which takes over lighting the sign the moment the mains goes down. Batteries used are usually NiMH or NiCd as those batteries are perfectly happy being trickle charged, don't try this with LiPo as you will destroy the batteries in the process. I don't know how LiFePO4 handles trickle charging.
It is interesting how you are so adamant against using available mains power, as this plus backup battery is simply the most reliable power solution available. You don't even have to remember to change the batteries every year or so. Being able to hook up to mains even allows you to use mobile data connections to send warning messages.
Mind, that backup battery doesn't have to work for very long upon loss of mains. A few hours is more than enough to detect the smoke, send out the warning messages, and then just sit there until the fire consumes it before the batteries run out.