They are crimp on connectors. There are usually two tabs on the connector that are forced around the bare wire and smashed down with a special tool. There is usually a second set of tabs that crimp onto the wire insulation for strain relief. They are generally not re-usable, but you may be able to dig out the old broke off piece of wire and solder the wire back onto the connector. There maybe a barb tab on the side or top of the connector to allow you to get the pin out of the plastic shell.