Explanation:
The sentence contains a B. comma splice fault and requires a conjunction.
This is the reason why:
An incomplete sentence without a subject or verb is called a fragment. The verb "ran" and the subject "The cat" are both present in this phrase.
A run-on sentence only has a comma to divide two independent clauses. The two independent clauses in this statement are "He was gone for three days" and "The cat ran out the back door."
Specifically, a comma splice is a run-on sentence in which an independent clause is erroneously linked to another clause with just a comma. In this sentence, this is true.
You can correct the statement by adding a conjunction:
"The cat disappeared via the back door and wasn't seen for three days. " (This uses a coordinating conjunction to form a compound sentence.) "The cat raced out the back door. He left after three days. (This uses a full stop to divide the two independent clauses.)
Both choices express the intended meaning and are grammatically sound.