Im like those above – the way Emma talked about him seems like she’s protecting not only Henry from him but herself too. She also told MM to trust her, dont get involved with a married man, so Im thinking he must have been in a position of power (of some kind) over her & used that to his advantage (very likely he was married) & she ended up taking the fall for it or something, as the guy must have done something REALLY off for Emma, who desperately wanted a family of her own (she said shes been searching for her family since she was a kid), to not only not tell him she was pregnant & cut all ties with him, but also to tell Henry he’s dead & so ensure he wont ever go looking for the guy either.
If he was just a bum, loser or petty thief, all she’d have to do is look him up & find out where he’s at (its not like she doesn’t have the skills to do so) in order to see if he’s changed his spots or not- yet she choose to end ALL association with the guy, that’s not something you usually do on a whim.