Will the smoke alarm stop beeping if the battery runs dry?

Eventually the battery will go flat and the beeper will stop, but a high-pitched sounder takes very little power, and it only beeps a few times now and then, so it could take days or even weeks. Do you know any friends or relatives of your neighbour who might know where he is ? I'm sure he wouldn't want his alarm to bother you., but on a more serious note, the alarm will alert people to the fact that he's not at home.

If you want the noise to stop, you might prefer to tell them that you have seen a suspicious looking character hanging around.

If your neighbour thinks there might be a break-in he will be keener to turn his alarm off.

If new batteries don't stop it I'd suggest new smoke alarms. The radioactive material in them only lasts so long and they probably wouldn't work correctly in the event of a fire anyway. If / When you get new ones, get at least one that also has a carbon monoxide detector built in - this is a colorless, odorless gas that can be fatal if you are exposed long enough.

eventually, because the power source will be non existent