body jacket

noun2

1. •
   A form-fitting garment covering the upper body, with or without sleeves.

   • Young Grimaldi, in a white body jacket, plays off several antics at the end of the first act […] — 1824
2. •
   A rigid brace that fits around the torso (but does not cover the neck, arms or legs) to immobilize the spine, reduce curvature, etc.

   • When the goal is to provide postural support, slow progression, or postpone (but not prevent) surgery, a polypropylene body jacket, or “clam-shell brace,” may suffice for waking or sitting hours. — 2000