"Falling economy" and "failing economy" are similar ways of describing a situation where unemployment is rising. There an usually an increase in government spending causing an increase in the deficit since the government cannot raise enough revenue to stay out of debt.
P.S. It seems Robert and I agree on this. He got his post in first.
I don't agree with you because I don't remember the source of sentence but it is probably from an important dictionary publishing. But I know some people call a famous one as Wrongman which is in harmony with its name and I think you guess it.