Do you suspect a broken wire inside a connector? Try to unscrew the barrels on the plugs (called banana plugs in the USA). A broken wire could be gripped in a strain-relief, hence it doesn't necessarily come loose.
Cut away insulation to expose about 3/16 inch of bare wire end. Solder it back.
They are not usual cables for the speaker. They are commonly audio signal cables. If the cables are at fault, they must be broken (discontinuous) inside- just check with a multimeter.
They are cheap and easily available. It may be simpler to replace than to repair the connector. The connectors appear to be moulded in place.