Connecting a surround system without jacks
Most sound systems have speakes with terminals and custom cables with a custom connector at one end and bare wire at the other. Just connect the speakers to the existing wires as usual, and connect the custom wires to the other end with soldering or with a screw terminal. I also have this configuration in my living room and it works perfectly.

Anyway, even if the speakers are hardwired to the device, you can still cut the wires and connect them to the installed wires with screw terminals.

And I believe the phrase you're looking for is "speaker terminal".