Lack of joist hangers will not necessarily cause the floor to sag. Many joists rest on sill plates and are blocked or joined with a rim joist rather than placed in a hanger. A few answers to questions would help.
Is the floor dropping down off a sill plate or beam, or are they sagging in the center of the span?
Is the problem on a first or second floor?
Does the house use conventional or balloon framing.
What is the span in feet and what dimension of joist is involved?