MSP to MP3 sub?

Yea so the blue and white stipe wire gous connected to the back of stereo. What if I spliced it can i connect it back. And can I use any wire for the power cord b cus the yellow wire was to short so i used the redwire to make it longer which was about the same guage. Can I use that same wire to connect the ground since it came with no ground wire.
 
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