Can a sentence contain a subject and a verb but still be a sentence fragment?

Yes, a statement might have a subject and a verb but still be a sentence fragment. This is especially the case with dependent clauses. When a dependent clause is not connected to an independent clause, it is a sentence fragment:

  • When Alex had a birthday party.
  • When Alex had a birthday party, I was able to help with the arrangements.

To help you decide, you need to ask yourself if the clause expresses a complete thought (e.g., “When Alex had a birthday party, I was able to help with the arrangements”) or if there is information missing (e.g., “When Alex had a birthday party”).