Barnes has some useful comments about what we find in the LXX on Job 2:9.
Then said his wife unto him - Some remarkable additions are made by
the ancient versions to this passage. The Chaldee renders it, "and
"Dinah" (דינה dı̂ynâh), his wife, said to him." The author of that
paraphrase seems to have supposed that Job lived in the time of Jacob,
and had married his daughter Dinah; Genesis 30:21. Drusius says, that
this was the opinion of the Hebrews, and quotes a declaration from the
Gemara to this effect: "Job lived in the days of Jacob, and was born
when the children of Israel went down into Egypt; and when they
departed thence he died. He lived therefore 210 years, as long as they
were into Egypt." This is mere tradition, but it shows the ancient
impression as to the time when Job lived. The Septuagint has
introduced a remarkable passage here, of which the following is a
translation. "After much time had elapsed, his wife said unto him, How
long wilt thou persevere, saying, Behold, I will wait a little longer,
cherishing the trope of my recovery? Behold, the memorial of thee has
disappeared from the earth - those sons and daughters, the pangs and
sorrows of my womb, for whom I toiled laboriously in vain. Even thou
sittest among loathsome worms, passing the night in the open air,
whilst I, a wanderer and a drudge, from place to place, and from house
to house, watch the sun until his going down, that I may rest from the
toils and sorrows that now oppress me. But speak some word toward the
Lord (τι ῥῆμα εἰς κύριον ti rēma eis kurion) and die."
Whence this addition had its origin, it is impossible now to say. Dr.
Good says it is found in Theodotion, in the Syriac, and the Arabic (in
this he errs, for it is not in the Syriac and Arabic in Waltoh's
Polyglott), and in the Latin of Ambrose. Dathe suggests that it was
probably added by some person who thought it incredible that an angry
woman could be content with saying so "little" as is ascribed in the
Hebrew to the wife of Job. It may have been originally written by some
one in the margin of his Bible by way of paraphrase, and the
transcriber, seeing it there, may have supposed it was omitted
accidentally from the text, and so inserted it in the place where it
now stands. It is one of the many instances, at all events, which show
that implicit confidence is not to be placed in the Septuagint. There
is not the slightest evidence that this was ever in the Hebrew text.
It is not wholly unnatural, and as an exercise of the fancy is not
without ingenuity and plausibility, and yet the simple but abrupt
statement in the Hebrew seems best to accord with nature. The evident
distress of the wife of Job, according to the whole narrative, is not
so much that she was subjected to trials, and that she was compelled
to wander about without a home, as that Job should be so patient, and
that he did not yield to the temptation.
The Cambridge commentary is more succinct:
The Sept. introduces her speech, which it gives in a greatly amplified
form, with the words “when a long time had passed.” The amplification
is not unsuitable to the circumstances, but the curt phrases of the
original are truer to art and nature, for grief is possessed of few
words.
The Keil and Delitzsch Biblical Commentary on the Old Testament is more dismissive:
In the LXX the words of his wife are unskilfully extended. The few
words as they stand are sufficiently characteristic. They are not to
be explained, Call on God for the last time, and then die (von Gerl.);
or, Call on Him that thou die (according to Ges. 130, 2)
The addition appears to have its origin in some commentary that has (unfortunately) found it way into the text. The origin of the addition is now lost so we do not know whether it was originally Hebrew or Greek. I would favor the latter.