Let’s look at two examples: older incandescent lamps and newer electronic bulbs, namely CFLs or LEDs. Let’s say that the light output is not sufficient or it is insufficient.
The classic incandescent is the first.
An incandescent has only one working part. It is the filament. If it fails, it will break. It cannot use electricity if it breaks because no current flows when it is broken.
Electronic bulbs, also known as CFLs or LEDs, are the other possible cases.
CFLs and LEDs may fail while drawing current.
The reason they can still draw power is the power supply components or the light driver circuit may still be active or have failed in some current drawing way even if the light emitting element is burned out, This is one of the disadvantages of new high efficiency lighting – it is so much more complex than the simple filament-is-the-only-part incandescent.
Aside note: I found once that a dead CFL (as in “not emitting lights”) pulled more current than its electrical rating. This is not a typical situation. A failed bulb will usually use less current than the rated current, or none at all.