If you have a garment that was specifically designated to be worn on Shabbos (or Yom Tov) are you allowed to start wearing it during the week if it has become worn out from repeated use and thus no longer proper for Shabbos?
According to this answer from Rabbi Yehoshua Pepper I do not see why one can not switch Shabbos clothing into weekday clothing once he is not wearing it for Shabbos anymore. The issue is to have exclusive clothing for Shabbos, if one makes it into weekday clothing it is not for Shabbos anymore.
Items that are meant to be used for personal use, even if that use is a Mitzvah, are allowed to be used for personal use when the mitzvah is no longer applicable. For instance, although we find that the leftover oil and wicks from Chanuka are not allowed to be used for personal use, shulchan aruch 677 4, we find no such law by leftovers from shabbos lights, which were instituted specifically to be used. Another point is even the leftovers from Chanuka lights can be used as long as they were used to complete the mitzvah. Only oil from that first half hour is muktza, if however it burned for the half hour, the leftovers are permissible for mundane use, see there and siman 674 siff 2. So clothes which served their full duty would be the same.
One idea though which you can take into consideration is something that is written in the Orchos Chaim from R' Aharon MiLunil in the beginning of hilchos shabbos, laws for erev shabbos #9. He says a chidush not found anywhere else that the reason to wear special clothes on shabbos is to be a reminder that the day is holy and it is not allowed to do melacha. Taking his words into consideration, if wearing leftover shabbos clothes would confuse this distinction, it might be better to avoid doing it.
I'm not following the context / reasoning behind your question. Clothes do not get a "huktzah lemitzvah" status (attached to a specific mitzvah or purpose) with regards to wearing it for Shabbat. People wear their Shabbat clothes midweek often. My son has about 50 identical white shirts (don't ask me why!) I know that he doesn't have shirts specifically marked "Shabbat only".
If you can wear a Shabbat shirt during weekdays when it is good, why can't you wear it when it's worn out? As to whether you should EVER wear worn out clothes - that's a separate question that you're not asking.
If I'm missing a factor in the intent of your question, you may wish to edit and clarify it.