"He refused the offer, a decision which proved to be disastrous."
is contemporary English for, and with the same basic meaning as:
"He refused the offer, which decision proved disastrous."
The issue for me is having only "He refused" followed by a comma and then the clause. As is the case with the OP's fragment: he refused, which decision proved disastrous.
I would accept:
- They made him the offer. He refused.
- They made him the offer. He refused it.
I don't accept:
- They made him the offer. He refused, which decision proved disastrous.
- They made him the offer. He refused, a decision which proved disastrous.
I would accept:
- They made him the offer. He refused it, which decision proved disastrous.
- They made him the offer. He refused it, a decision which proved disastrous.
Refuse on its own is commonly used without anything after it in response to a question's verb.
- Do you accept to go?
- No, I refuse [implied: to go].
- Yes, I accept [implied: to go.]
- Yes, I refused to go, which proved disastrous.
The which clause (above) is anaphoric to the main clause. If we don't
have the refuse to go, it would not make sense. It's interpretation
depends on the entire antecedent's meaning.
- Do you accept the offer?
- No, I refuse it.
Generally, one would not create a sentence with the verb refuse unless it contains either a direct object or verb-to-verb structure (such as:) He refused to go, which was a problem. He refused the tea, which was a problem. One wouldn't write: He refused, which was a problem. Unless it is a novel or a dialogue of some sort.
That is because refuse and accept (and probably others) become anaphoric and require the full verb phrase (refuse to go) to make it make sense.
Also, the OP's question is not a dictionary "entry", as far as I can determine.
It is on some dodgy sites.
This is an example of a grammatical use of the which determiner, with ineffective instead of disastrous:
"The Supreme Court of Ohio, after this abundant and most extraordinary proof before them, ignored the people's sacred right of eminent domain, and simply decided that these roads be ousted from charging less rates per 100 pounds on tank car shipments, as compared with barreled oil, which decision proved ineffective."
the phrase refers to "simply decided that these roads"
EDIT to my answer: Please go to this site and look at how the verb refuse is given in examples to English languages learners. There is refuse with nothing after it, refuse with a direct object (noun) and refuse followed by verb +to+verb.
use of the verb refuse in English
Those examples basically confirm what I have been saying about the verb refuse.
[Please note: The OP has now posted the page from his Mac. The phrase is can only be called a Mac disaster. If the page reproduced in the question is an example of what is on Mac computers, Apple should be ashamed of itself. Really. I'm speechless. Speechless! No wonder I have to work so hard, and I don't mean here. I mean correcting translations into English.]