How to fix a broken sub connection and wire?
These are Faston connectors, or similar. (Faston is a Brand name of TE Connectivity.)

This one is to be crimped on the speaker's wire.



Although you can fix the wire with a pair of pliers too, I would recommend to use the purpose-made crimp tool for it, as the connection will be a lot more reliable. These tools can be pretty expensive, but maybe you can borrow one. Fix the crimped Faston to the speaker's frame with Tec 7 or something similar.  

Note that Faston exists in different tab widths, make sure you buy the right size.