It is considered a disgraceful to take an item that had been used for a mitzva (such as shofar, lulav and tzitzis) and use it for a mundane purpose if it can still be used for the mitzva. Therefore, as long as a garment is usable, its strings should not be used to tie other items. This holds true even when the garment is not being worn or is otherwise exempt from tzitzis. The same is true of a shofar or schach which are still reusable.
According to the Mechaber, items that were prepared -- but not used -- for a mitzva, or items that had been used but cannot be reused, may be discarded. The Rama adds that according to some poskim, used mitzva items should not be placed in the garbage while other poskim require that they be placed in storage, and it is praiseworthy to be stringent. Other poskim recommend using reusing the items for other mitzva-related purposes, such as using a torn tzitzis string as a marker in a sefer. It is forbidden to put a used mitzva item to an offensive use.
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Using a talis for non-mitzva purposes
A talis garment is not in the same class as the tzitzis, and once the strings are removed it may be discarded. It cannot be used for an offensive purpose that would denigrate the mitzva. A wearable talis gadol may not be used for other purposes, but a talis koton may be put to non-offensive use. The contemporary poskim discuss whether wiping sweat or cleaning glasses are non-offensive uses.
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Only garments worn for the purpose of being dressed are required to have tzitzis. It is permissible to try on a four-cornered garment for size or demonstrate how it is worn without attaching tzitzis.
The halacha does not mandate that people own houses with doors requiring ?mezuzos. Chazal call mezuza chovas hadar-i.e. only someone who dwells in a house with proper doors is required to have mezuzos.
Chazal were concerned that a goy with tzitzis on his garment might be able to lure a Jew to accompany him on the road and then attack and kill him. Therefore, Chazal forbade selling a garment with tzitzis to a goy and even storing such a garment with a goy.