Does this sentence require the pronoun 'they'?

I have the following sentence:

There were several dominoes—some so precariously placed that I'd swear should have toppled over.

I believe it's correct, but when read quickly or out loud, it sounds kind of funny, almost like a "they" is missing.

There were several dominoes—some so precariously placed that I'd swear they should have toppled over.

My reason for thinking that the first sentence is the correct one is that if I strip the sentence to its essentials, the "they" definitely doesn't fit.

There were dominoes that I'd swear should have toppled.

Am I right in thinking that "they" is not required, or is there something incorrect happening here?

Solution 1:

You have apparently analyzed the that-clause as a Relative Clause (which wouldn't have a they)

• There were dominoes that I swear should have toppled over (no they)

This is a relative clause, as can be shown by substituting which for that, or deleting it altogether

• There were dominoes which I swear should have toppled over
• There were dominoes I swear should have toppled over

That's why you thought the they was not required.

But in the sentence provided, that is not a relative clause marker. This that is part of the

X be so Adj that S

Construction, where the S refers to a tensed clause introduced by a complementizer that, like that he can't think in

• He is so exhausted that he can't think.

This that is also deletable, but you can't substitute which for it.

• He is so exhausted he can't think.

• *He is so exhausted which he can't think.

So it can't be a relative clause. Furthermore, the S introduced by this that has to be a full tensed sentence, with a subject noun phrase, and with any object nouns or pronouns present also, since they haven't been deleted or moved by Relative Clause Formation. That's why it really does need the they.

There are several uses for the English word that, and it's easy to confuse the constructions they're in.

Solution 2:

The they is necessary in your first example:

There were several dominoes—some so precariously placed that I'd swear they should have toppled over.

But in your second example, they should not appear:

There were dominoes that I'd swear should have toppled.

You stripped the first sentence a little too far (so precariously placed is part of the "essentials") to get the second. A truer version would be:

There were dominoes so precariously placed that I'd swear they should have toppled.

To explain the rationale behind using or not using they: in your first two examples, that is part of the conjunction so that, whereas in your third (stripped) example, that is a pronoun. Since in the latter case that is the noun, they is unnecessary (there is already a noun). Contrast this with the former case, in which so ... that is a conjunction separating two independent clauses (there were dominoes and I'd swear they should have toppled). The second clause needs to be a complete (independent) sentence, and therefore needs a noun, hence they.