Stereo cable entry broken...How to fix it?

Sadly Jawbone the company is not well these days: Jawbone is going out of business. Once they were quite innovative with there small speakers and bluetooth headphones.

Sadly, parts are just not available from them. I have seen a few eBay listings of some parts which is where you'll need to look.

Here's the IFIXIT guide to gain access to the assembly: Jawbone Big Jambox Micro USB Port Replacement

If you can desolder the jack socket you might be able to locate an off the shelf replacement at a good electronics parts supply house.

Maybe the better answer here is not to fix it and just use the Bluetooth connection.

Or, look at getting a new speaker. I had two Jawbone units both died, I went out and bought two UE Boom2's which I think are quite good!