Airbag light staying on?

You said it's fixed, so why would there still be a disconnected wire? Was there any mention of a diagnostic fault code? There had to be one to tell the mechanic where to start the diagnosis. If that exact code number was included on the invoice, tell me what it is and I can find the definition for you.

If the "Air Bag" light turns on for a few seconds when the ignition switch is turned on, then goes off and stays off, the system has passed all the self tests and is working properly. On most models, any fault codes have to be manually erased with a scanner so they don't remain set and confuse the mechanic the next time the system is worked on. Erasing codes after any repairs is standard practice, but on many systems, if the problem is repaired, the warning light can turn off even when a fault hasn't been erased. Is your warning light off now?