Saved her? Think about it, where is her life going to go now? She'll be a slave-made. She's going to be endlessly harassed by others who know she was a princess by those around her (her coworkers) also because her personality is likely to get on their nerves and what can she do about it? Not like any of the leadership will care about a fallen princess with no power. Furthermore, she's now at risk of being sexually assaulted. Again, no one will care about a slave/maid and she's also an appealing target cause "never had a noble girl before."
And what's the long term goal? If it doesn't do some bs, there's nothing she can really strive for realistically. She can't be anything more at this point than some mistress/concubine of a noble (and it's clear the prince is set up as the love interest which also bothers me). With her personality, think she'd be happy as a mistress/concubine? Prolly not. No noble will take her as a wife cause of her background (even if they don't know, nobles aren't gonna marry some one they view as a slave/commoner) and a lack of any family with status to support her/give her value to them.
I just don't see how this realistically would end up something positive for her, just endless abuse and suffering. It's not like women in general have much in terms of power in these kinda settings, especially a slave (which we know she is now).
I mean, I also think her getting over her realization that she's been hated this whole time by her people and her father was hated as well as being hanged (far as we can tell, it was her ONLY family too)... which means she's now completely alone. It's just kinda heartbreaking even if her normal personality is one of too much pride that makes her a person of poor quality.
This prince and his father are complete dumbasses to think this "helps" or "saves" her.