Question

Is what's below a complete sentence or a fragment?

Answer 1

Answer:

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.

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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.

Answer 2

It is a fragment.

Although it has a subject and predicate, it is a subordinate clause as it starts with 'especially', indicating an adjective or adverb clause.