Was the context for this quote ever provided? As far as I know,
which is not very far since I do not have and have not read the
volume, this is quoted from a volume that transcribes remarks
Hayek made at the American Enterprise Institute.  So first of
all, unless he reviewed and edited his remarks, it is not part
of his published and considered writing.

It probably (?) came to fame by being quoted by Haberler in
the Cato Journal a decade later.  (Haberler was an AEI resident
scholar.)  Appended is a fuller quote from Haberler (1986),
which provides more context.

Alan Isaac

Hayek now says there are two exceptions to the rule that changes
in aggregate demand do not affect the level of employment.
The first one was “an accidental historic situation.” In 1925 Britain made the
mistake of returning to the gold standard at the prewar parity, which
meant that real wages were too high. “In this situation,” he wrote,
“the restoration of employment required a reduction of real wages
which could he achieved by a general rise of prices” (1974, p. 4).

“The second situation in which it is true that an increase
of employment requires an increase in aggregate demand,” Hayek (1974, p. 5)
now maintains, “is found in the later stages of a depression
when, in consequence of the appearance of extensive unemployment, the
economy frequently is subjected to a cumulative process of contraction.
... of secondary deflation, which may go on for a very long
time.” He concludes:

     I am today the last to deny—that, in these circumstances, monetary
     counteractions, deliberate attempts to maintain the money stream,
     are appropriate..., I have to admit that I took a different attitude
     forty years ago, at the beginning of the Great Depression. At that
     time I believed that a process of deflation of some short duration
     might break the rigidity of wages which I thought was
     incompatible with a functioning economy. Perhaps I should even then have
     understood that this possibility no longer existed. ... I still believe
     that we shall not get a functioning economy until wages again become
     flexible, but I think that we shall have to find different techniques
     for that purpose.... Today I believe that deflation has no recognizable
     function whatever, and that there is no justification for supporting
     or permitting a process of deflation [1974, p. 5].