Even she is really only there to connect the reader to the story of the Hebrew youth Joseph.
The husband’s name possibly means “priest of the sun (or sun-god)”. He is called saris, which is normally a eunuch, but that translation hardly fits the story. He is a saris in the sense of a palace official. He is also called sar hatabbachim, “the chief of the butchers”, i.e. a royal executioner or military officer (cf. II Kings 25:8).
Mrs Potiphar tries to get Joseph to lie with her, maybe not so much to gratify her own instincts or to besmirch Joseph but rather to harm her husband for bringing the Hebrew into the house.
Who knows how fragile was the marital relationship? If the wife was annoyed with her husband she could have been looking for a way to ruin his reputation in the eyes of the royal court.
Whilst Potiphar had to take note of her accusations he was aware of her thinking. He did not execute Joseph but imprisoned him. Presumably his dignity was saved.
We would have liked to know his later history but that does not concern the Narrator as much as the fact that Joseph is now in a situation where he can save the empire, and that’s what the story really wants to expound.