What does to 'cry off' mean?

[Rich7]

Test No. incompl/inter-43 "A Crying Shame", question 5

We had great hopes of being able to invite the distinguished writer to our meeting but he cried ......... at the last moment.

(a) on
(b) through
(c) with
(d) off

Test No. incompl/inter-43 "A Crying Shame", answer 5

We had great hopes of being able to invite the distinguished writer to our meeting but he cried off at the last moment.

Correct answer: (d) off

Your answer was: correct
_________________________

I don't understand the whole meaning.

[Torsten]

We thought we would be able to invite the famous writer to our meeting but at the last moment he changed his mind and decided not to accept our offer.

TOEIC short conversations: Shopping for a deal

[Kati Svaby]

cry off=(BrE inf) to say that you cannot do sth that you promised to do.
-She said she was coming to the party, but cried off at the last moment.