Let's say I have the following sentence:
Yesterday the stock market crashed, which resulted in social collapse.
Is it grammatically correct to change the above sentence to the following form?
Yesterday the stock market crashed, resulting in social collapse.
If so, what is this progressive substitution called?
Yes, you may reword the sentence to use resulting, but that's not a progressive "form" (really, tense) of the verb. It's the present participle. The progressive forms of the verb to result sound a bit odd since a result is a conclusion. Let's try to run for contrasting examples:
Past progressive (main verb):
Stockbrokers were running around in a panic during the stock market crash.
Notice that although it's the present participle, it has formed a past tense verb referring to past time. Of course, it could form a present tense verb, are running.
Present participle (modifying Stockbrokers):
Stockbrokers running around in a panic caused the stock market crash.
Notice that although it's the present participle, it doesn't refer to present time (or time at all): it describes the state of the brokers. Presumably, the running around took placing before and during the crash, which is over.
Short answer:
No, a progressive form (present participle) can never replace which. Which is elided, not replaced.
Long answer:
It is so called an absolute construction (also known as a participle construction) or participle clauses where a subject is omitted when it is or is considered the same subject as that of the main (independent) clause and a finitive verb form is changed to a non-finitive form.
Yesterday the stock market crashed, which resulted in social collapse.
The subject of the relative clause headed by which is which. It refers to the "action of stock market's crashing yesterday" and that action resulted in social collapse. By eliding the subject which and changing the past tense form resulted to a non-finitive form (present participle) resulting, you can create a participle clause.
Participle clauses replacing a relative clause
A present participle clause can replace an active voice finite relative clause. The noun before the participle is the doer of the action:
If you think you have received an e-mail containing a virus, you should delete it immediately.
(If you think you have received an e-mail which contains a virus, delete it immediately.)
