Grammatical name for BEFORE HE COULD REACT [closed]

Solution 1:

I think the peculiarity that's being referred to in the sentence is the fact that before he could react presupposes that he did not, in fact, react. In other words, before is negative in this construction, and denies the clause it introduces.

This particular construction has been well-documented and is called the Counterfactual use of before in the literature. It often uses can or could to emphasize impossibility, but that's not necessary, viz:

• Get him out of here before anybody sees him.
  (Note the negative polarity item anybody, triggered by Counterfactual before)

Success in the endeavor could be reported as

• We got him out of there before anybody saw him.
  (which entails that nobody saw him)