Final answer:
A. Yes, this is a run-on sentence. It can be fixed by adding a subject and a verb or by turning it into a subordinate clause.
Step-by-step explanation:
Yes, this is a run-on sentence. A run-on sentence is when two or more complete sentences are not separated by any punctuation. In this case, 'The next-door neighbors of my elderly grandparents.' is a sentence fragment because it does not have a subject or verb.
To fix this, you can add a subject and a verb, or you can turn it into a subordinate clause by adding a subordinating word like 'who' or 'that'.
A run-on sentence consists of two or more complete sentences that are not properly punctuated or connected. However, the sentence in question lacks a verb and does not express a complete thought, which makes it a sentence fragment.