What happens if I accidentaly inhale food?

Factual Questions
1

So, I was eating prezel sticks(prezel cigars) and I was thinking, "What happens if I inhale the dust or the little chunks of the sticks?

For that matter, what happens if you inhale other food, of a more sizeable matter, but not enough to block the airway?

How does it get out of your lungs?

2

Same way other particles get out – you cough 'em up sooner or later.

3

Alternatively, it lodges in your lung and becomes a focal point for bacterial growth, leading to nasty things.

A bunch of things you probably did not want to know can be found in this article on aspiration pneumonia.