Dependent clause and use of subordinate conjunction

Question

A subordinate clause—also called a dependent clause—will begin with a subordinate conjunction or a relative pronoun and will contain both a subject and a verb. This combination of words will not form a complete sentence. It will instead make a reader want additional information to finish the thought. (From a grammar website).

Are there any instances which contradict a dependent clause beginning with a subordinate conjunction or relative pronoun as written above.

He arrived late for work again, not that it mattered. (for example).

Answer 1

In relative clauses, the relative pronoun can be deleted if it is not the subject of the clause. E.g. The woman (whom/that) we hired has excellent references.

Also, some relative clauses start with a prepositional phrase, with the relative pronoun being the object of the preposition. E.g. The woman with whom I spoke was very helpful.

Im sure there are other examples.

Answer 2

Firstly the statement stated, “...will begin with a subordinate conjunction or a relative pronoun...”.

There is a contradiction to the claim that a subordinate clause must start with a conjuction - it is not necessarily must be.

I told him that he should see a doctor. - here ‘I told him’ starts perfectly fine without the relative pronoun as a start.

Is poor although he dresses nicely. - same as above - starts perfectly fine without a conjunction.