Electricity follows the path of least resistance, so if the regular grounds are not good it will use the cables as its ground source.  As you can see the size of a normal ground strap is much larger than the other cables. The small cables are actually melting and then breaking from the voltage passing thru them.   Its also a good idea to clean all the electrical connections that you can. Most of our cars are 30+ years old and have some corrosion built up.