Is what's below a complete sentence or a fragment?
Especially when Jesus Foster almost dropped the birthday cake when all the candles were lit.

a fragment

Explanation:

In the same way that my answer above is a fragment, the given sentence is a dependent clause, and as such, it cannot stand on its own; something must either be added to it or deleted from it.

fragment:   a fragment

complete sentences:  

It's a fragment.  

A fragment is a only a piece of a complete sentence.

fragment:    Especially when Jesus Foster almost dropped the birthday cake when all the candles were lit.

complete sentences:  

Jesus Foster almost dropped the birthday cake when all the candles were lit.    

I laughed a lot at the party, especially when Jesus Foster almost dropped the birthday cake when all the candles were lit.

the correct answer is the first one.