TT #292 · Parshas Tazria · Aliyah 7 · Passuk 55
English: The priest shall examine the lesion after it has been washed; if the lesion has not changed in appearance and has not spread, it is impure; you shall burn it in fire. It is a penetrating decay, whether the worn or unworn side is affected.
Torah Temimah cites Sanhedrin 88a for deriving the garment rule from the parallel rule for a person.
E-Daf — Sanhedrin 88a · Shas.org · Sefaria — Sanhedrin 88a, source text and translation
English: The same terms, “karachas” and “gabachas,” appear for garments and for people. Just as a person whose affliction spreads over the whole body is pure, so too a garment whose affliction spreads throughout is pure.
Textual derivation
Just as a person whose affliction covers the entire body is declared pure under the parallel rule, a garment whose affliction covers its entire surface is also pure.