What allows the omission of subject relative pronouns?

All but one of these sentences starts with a phrase saying something exists:

There's …
There is …
That's …
I have a …

I could easily be wrong about this, but my gut feeling is that this is what allows the informal deletion of the subject relative pronoun, although the constructions with it deleted definitely feel informal to me. Taking examples from grammar websites and deleting the subject relative pronoun, in general I find that the only ones I feel work well are those starting with such an existential construction.

I told you about the woman lives next door.
This is the house had a great Christmas decoration.

The following sentences don't work for me when you drop the "who", although maybe it's just because they're more complicated.

*It took me a while to get used to people (who) eat popcorn during the movie.
*The world is a much sunnier place for people (who) have a positive attitude.

These are all colloquial forms of speech that do not conform to formal rules, are technically incorrect, but are readily understood. People talk this way.

While not dogmatically, I suggest the colloquial nature of the phenomenon is probably a regional and/or cultural thing. I would never (well, never say never) use that construction but would opt for the following versions, even in informal contexts:

• Some men won’t even look at a girl with a baby.

• A young student comes here some evenings.

• That smell could raise me out of a concrete grave.

• I guess Cal asked Lee.

• A friend called me yesterday.

In short, what "allows . . . the omission," as you put it, is artistic license, or "that's the way people talk around here"! (That reminds me: one of the best and shortest definitions of culture is, "Culture is the way we do things around here.")