What does it mean when someone is on the borderline?

Answer 1

He's between two different states of health or behavior.

http://www.google.com/#q=borderline+definition

What is the context of this use of borderline?

Answer 2

I'm talking about money when a person is almost destitute. Is that context okay?

Answer 3

He's on the borderline between being destitute and able to support himself.

Answer 4

Yes.