Why can the relative pronoun be omitted?

Question

Look at the sentence:

—> That’s the actor who was a pilot in Star Wars. The relative pronoun is the subject so we cannot omit it. I know that we can omit the relative pronoun if it’s the object.

My question is : Why can the relative pronoun be omitted from these following sentences ?

1) —> My brother, who is a former professional hokey player, coaches elite high school hockey. becomes: —> My brother, a former professional hokey player, coaches elite high school hockey.

2) —> Teachers who work online have flexible schedules. becomes: —> Teachers working online have flexible schedules.

3) —> The man that was bitten by the dog went to hospital. becomes: —> The man bitten by the dog went to hospital.

Answer 1

[1a] My brother, who is a former professional hokey player, coaches elite high school hockey.

[1b] My brother, a former professional hokey player, coaches elite high school hockey.

[2a] Teachers who work online have flexible schedules.

[2b] Teachers working online have flexible schedules.

[3a] The man that was bitten by the dog went to hospital.

[3b] The man bitten by the dog went to hospital.

You're not omitting the relative pronoun, but replacing the relative clause with a noun phrase or a different kind of clause:

In [1b] with an appositive noun phrase, in [2b] with a gerund-participial clause and in [3b] with a past-participial clause.

Answer 2

My question is : Why can the relative pronoun be omitted from these following sentences?

If you look at your sentences, it is not only the relative pronoun that is missing, but the linking verb is also missing. Thus we have

1. The running man was the thief. - Running is a "participle modifier" - a participle that modifies (adjectivally) "man".

2. The man running was the thief. - Running is a "participle modifier." This construction is also known as a reduced relative clause. (It is "reduced" by the omission of "who/that was")

3. The man who/that was running was the thief. - who/that was running is adjectival (otherwise known as a relative clause as it describes the man adjectivally)