Is there a term for a sentence with no (or implied) subject? If so, what?

Take this from Nick Cave's song 'Higgs Boson Blues':

She curses the queue at the Zulu. And moves on to Amazonia.

Is there a term for a sentence without a subject, or where the subject is implied from the previous sentence, like

And moves on to Amazonia.

This Quora (https://www.quora.com/In-formal-English-is-it-grammatically-correct-to-use-sentences-without-subjects-as-in-Went-home-late-Ate-biscuits) suggested that imperatives and exclamations often omit the subject, but the above sentence doesn't seem to fit as either of those, as it isn't an direction (like an imperative) or really exclaiming anything.

Is there a term for a sentence that has no subject, or implies the subject from the previous sentence?

Answer

"Sentence fragment", "dependent clause", and "phrase" apply, here. What you have there is improper punctuation of a single sentence.

A "clause" is a section that has subject, verb, and whatever objects are required. A "phrase" is any chunk that holds a distinct meaning as a group. A "sentence fragment" is a clump of words masquerading as a sentence but that can't actually fulfill the requirements. A "dependent clause" requires another clause to function.

Your example's first part can stand alone, but the second part is a "dependent clause" since it 'borrows' the subject of the former to function.

(In this case, the reason the dependent clause appears to be a sentence is that it has been punctuated the way it has. Thus, this isn't a grammatical error but typographical.)