If your chair back got loose, there’s an easy way to fix that.
All you need to do is to fix the holding screw.
Unscrew the bolt, spread superglue evenly on the thread, and screw it back very tightly. Let dry, and you may use the chair.
If you ever need to unscrew that, apply some nail polish remover to the threading and let the glue dissolve. You should easily unscrew the bolt after that.