iirc it was not mentioned how she died, it may be bcs og penny looked and acted like a dead person that made the duke think she's dead. as to the dukes feelings, he was def sad and felt regretful to the og penny though he didn't know she act died and our penny reincarnated into her. note that og penny is also our penny so basically they are the same person.
Imo he's wearing a mask like almost everybody to hide his shame and doubtfulness. Replacing his daughter didn't work to loose his grief and only hurt his sons who blamed Penelope for this replacement. But he couldn't just throw her in the streets, while doubting if what he did was right, all he did couldn't change what happened, so I guess he just gave up.
Ps: What he did was awful and Penelope suffered hunger like when she was in the streets, the only thing that changed was the pretty dresses and jewelry
i read the novel but not until the end and maybe i have forgotten details from past chapters, but i'm curious as to how the duke felt when the OG penelope died in the OG setup (game). was it mentioned in the novel? was he sad bc it seems like he actually cared for her even when they had a falling out?