Answer
See below.
Work Step by Step
When a lightbulb "burns out", the filament has broken/snapped, or chemically disintegrated.
There is no longer a path for current to flow.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.