Dropping "is" / "are" with dropping "that"

The word that is often dropped in an informal speech.

But what about dropping is and are? Consider the following examples:

1. Examples that are not intended to be used in real documents: ...

2. Examples are not intended to be used in real documents: ...

3. Examples not intended to be used in real documents: ...

Are both 2 and 3 correct?

1. Fragments ('that...' in that phrase is a relative clause modifying 'Examples')

2. Clause (You have Subject and Predicate there)

3. Fragments ('not intended...' is participle phrase modifying the 'Example')

Note: Fragments aren't complete sentences as fragments are usually mere Subjects.

I hope this simple explanation is comprehensible.