What is the 'libās at-tabadhdhul' (everyday clothes worn at home), to whom is a woman permitted to appear in it, and is there a specific time or situation that permits wearing it?

Linguistically, "tabadhdhul" (تبذل) means abandoning adornment or modesty. Terminologically, it refers to wearing "libās al-badhlah" (لباس البذلة), meaning work clothes, which are garments worn during work and service. Its terminological meaning does not deviate from its linguistic meanings.

It is disliked for either spouse to appear disheveled before the other, and it is recommended for both to adorn themselves for the other, based on the Almighty’s saying: "And live with them honorably" [Quran 4:19], and "And due to them [the wives] is similar to what is expected of them, according to what is reasonable" [Quran 2:228].

As for the ruling on a woman wearing "libās al-tabadhdhul," it revolves around covering the 'awrah (intimate parts). It is not permissible for a woman to wear it in front of non-mahram men because it does not protect her from exposing some of her limbs. However, in front of mahram relatives and women, there is no harm in wearing it as long as it does not reveal any part of the 'awrah. If it reveals any part of it, then wearing it in front of them is prohibited.