Fragments are incomplete sentences; so, they are also incorrect. Two common types of incomplete sentences are often use, especially in speaking.
Every clause must have at least one subject and one verb. If one of them is missing then the clause is considered a fragment.
Me, my wife, and my daughter.
The above sentence doesn’t have a verb. The sentence should be something like “Me, my wife, and my daughter went to Vietnam.”
In the middle of May stop working.
The above sentence doesn’t have a subject. The correct form of the sentence will be “In the middle of May, I will stop working.”
A dependent clause can’t be a sentence by itself. A main clause is always required.
Although, they had been living in Vietnam for years.
There isn’t a main clause. The above “sentence” can’t be considered a sentence. The correct form should be “Although, they had been living in Vietnam for years, they moved out.”
The family that lives next to us.
The verb in the main clause is missing. The sentence should look something like “The family that lives next to us are from Sweden.”