Why is one lightbulb in a string illuminated?
Figure 1. The intriguing light bulb has caught the attention of Smokey the Bear too.

There can only be a few possibilities:


The lamps are spread across several phases or split phases, the other phases are off and all but this lamp has blown. This is very unlikely.
Some joker has installed a battery powered lamp. This too seems unlikely.



  "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Sherlock Holmes.



The impossible has happened and all have blown but one. This could happen with an overvoltage - by lightning, for example. Some combination of poor contact, tough filament, arcing in another lamp (which would limit the voltage), etc., may be enough to let it survive.




Another possibility is that the power is on and that each bulb has its own light sensor (like some streetlights) and this one is the first to switch on. Again, unlikely.