If a mason leaves his lodge because he relocates and is not active in any other lodge for a period of time for whatever reason, would it be wrong for him to still, while not being part of any lodge, wear his masonic ring or have a masonic sticker on his car/computer etc.
As Brother Glen said, it would depend on the rules in your grand jurisdiction. Typically, to leave your Lodge, you would need to either demit or withdraw. Until then you stay on their books and would continue to receive an annual dues statement. If you fail to pay dues for a two-year period, you are subject to being suspended for non-payment (SNPD), and would be the same as a suspended Mason until you catch on our dues, at which time you could be restored to normal status. While suspended, you may not participate in any lodge activities, and you may not wear the emblems or regalia of the fraternity.
A Brother who demits or withdraws from his Lodge, and does not affiliate with any other lodge, is knows as a "Mason at large." Here in Arkansas, for example, if a Mason at Large does not affiliate with a regular Lodge within one year, places him in the status of a "willful nonaffiliate" and Masonic communication with the at-large brother is cut off and prohibited until he changes that status by joining a regular Lodge. (After one year, the fellow would no longer have a valid dues card, and would be detected by that means.)