Is there a good physical model for what happens when a light bulb suddenly goes out?
Incandescent bulbs fail because the filament wears out and gets too thin, and then breaks. DC filaments also suffer from uneven wear called "notching".

Since the filament gets thin and brittle over time, it tends to fail when mechanically shocked ( for example at turn-on when the resistance is low).  

There is a distribution of lifetime that is an exponential function of filament voltage. You can find models in some of the old GE literature if you look. Here's another article which covers some aspects of your question.