A new square taper BB can be had for $25 if you shop around. Your LBS may have one in the correct size but will likely be $35-40. If you have your own BB tool you can replace it no problem.
In any case this looks to be the non-drive side plastic retaining ring. The only purpose it really serves is to prevent the BB from torquing fore/aft or vertically, not laterally. The drive side is metal and is welded to the BB, the drive side holds it in place and the non drive side is effectively just a shim to keep it from torquing as you pedal. As long as it is still threaded in and the plastic completely surrounds the cartridge you will be fine to ride it tomorrow, but replace it when you can. Theoretically you dont really need the ring(on a steel frame) unless you are heavier than about 140lbs.
Also because it doesn't serve to hold the BB in place or prevent axle from having lateral wiggle this plastic retaining ring doesnt need to be "tightened" it should just be snuggly against the BB shell on the frame. It is made of plastic because it doesn't need to withstand any serious forces. Don't tighten it so much next time.