I have a chair with a broken back, it can be detached from the rest of the chair and has a metal piece that goes into the padded/cloth part of the back.
Chairs can be a bear to fix. Depending on what piece broke, it usually indicates metal fatigue from low quality steel used at high stress points (an engineering short-sight). On those kinds of chairs I just take off the broken pieces (arms, if any) and use the bottom as a roll around stool, cause fixing them only redistributes the stress load to another weak spot. They can be handy in the shop for working on the car (waxing the lower half and polishing the mags, etc.)
