Some of the older stereos actually used a "Chassis ground" on the back. If you actually took it off the stereo you removed I would just tape up the end and put it back. Never know if you need a good ground wire. Then just run a normal ground wire for your new stereo. If you didn't unbolt it and it was just in there then someone may have been running a small amp under the dash. They probably just left it there. Again just tape it up and tuck it back in there.
DISCLAIMER; If you want the quick fix do it as listed above. If your a perfectionist or having that wire loose bugs you, I would figure out where it ends and disconnect it from there.