My dads putting his 2005 ltz400 back together..and can’t figure out where this battery connection goes ...

 

Don't know the LTZ but a black with white stripe is usually an earth in Suzukiland so if that wire comes from the earth post on the battery there will be a matching bullet connector somewhere sticking out of the loom. On the 700KQ the wire goes to the coil, only know that because I had one one burn that wire out, no idea why. Of course it could be for an option not fitted to your machine.