
According to the novel her face is injured so much that they couldn't identify her. She didn't have much money so she got only the basic necessities and ate potatoes. She was actually found not like in this story were she walks out without any injury to the gaurds.
These chapters doesn't give justice to the internal turmoil faced by Edith regarding everything and the decisions she will make in the future.

The duke is a terrible father, favoring one child over the other but don't worry he will have his time in the future.

He does get embarrassed, but during the time the story is set getting embarrassed for such a big mistake made by a person such as him is huge enough for him to loose his face.
From what i remember after all went down, the duke and his wife doesn't go out much and just sits at home wallowing in their wrong decisions.
I think an aftermath like that is the most fitting for them than dying or anything.
Spoilers from the novel
1. MC and ML will have a happy married life as a Count and Countess of Ryzen. They have 2 children , a boy and a girl. The people at their place loves them. Boy is the older one, quiet and reserved, girl is the younger one, tomboyish.
2. Cliff will have his marriage annulled by the Emperor's order. And remarries after some years to a brown haired, green eyed daughter of a Count.
3. The author, aka Lize tries to get close with people using extravagance, even the Crown Prince but fails. Finally she tries to fake a person as the kidnapped Nephew of the Emperor but they found out it's a lie and sentenced her to prison. Edith helps reduce her death sentence to a sentence of her living in a monastery for the rest of her life.
4. Edith found the real Nephew and the boy meets his mom and has a tearful reunion. This was when emperor granted her a favor and she uses it to spare Lize's life.
5. Edith implements health insurance scheme in Ryzen. Also Edith got to see what happened in her past life after her death.
She saw every one regretting and the ones she thought who hated cry for her and vice versa. She finally let's go of the relations she had with them.