Can that be used to describe somebody running out of money other than feeling down/depressed?
Please supply some context.
A physicist talking about the Doppler effect may describe light waves as "being shifted into the blue".
Sometimes we talk about someone who has left without saying where he is going as having "disappeared into the blue". I'd guess this comes from the fact that the sky is blue, and we imagine him flying off into the sky and disappearing. But I'm just guessing about that.
In a specific context it could mean all sorts of things. Like, "When job applicants arrive, put forms from people with experience in the green box and those with no experience into the blue." "She wasn't sure whether she should wear her green dress or her blue dress, but after some hesitation she slipped into the blue." "Picasso's paintings tended more and more into the blue during this period." Etc.
The phrase "being into the blue" is not a set expression in English, and by itself does not make much sense to me.
feeling blue is the phrase you are thinking of for feeling down/depressed.
in the red is the phrase you're looking for for being in debt/making a loss. The opposite of it is in the black.
There are various other set expressions using blue, but none I can think of that involve losing money/being in debt. Into the blue itself, if pressed, I would associate with the sea/sailing - as "the blue" is sometimes used to mean the sea.