(Spoiler warning because I'm not very good at doing the hidden spoiler text thing.)
So as you can see in a synopsis from moviespoiler.com (and as somebody already mentioned), the Baker does learn that his wife is dead:
The Baker, Little Red, and Cinderella are waiting for the Baker’s
Wife to return. The witch appears with Jack, who has the Baker’s
scarf with him, revealing he found the Baker’s Wife (dead) at the
bottom of a cliff.
As mentioned before, Into the Woods doesn't tie the ending up with a neat little bow - and does so on purpose. We're not even supposed to know how they're going to manage to piece their lives together again, or even if they will manage - just that they have hope and are going to try. The Baker explicitly states that he will take in the kids (Jack and Little Red), since their parents and guardians are no longer there to take care of them. Cinderella does offer to join in with their new little family - but in a very platonic way, saying that she can pitch in by cleaning house. To quote the aforementioned summary again:
Jack and Little Red Riding Hood suggest moving in with the Baker. Jack
then invites Cinderella. She agrees, saying she can help clean the
house, which she actually enjoys.
Keep in mind that both the Baker and Cinderella have just had very difficult ends to their marriages - the Baker through the death of his wife, and Cinderella through learning of her prince's infidelity and essentially parting ways. At the end of the story, neither of them is likely in an emotional place to bring a new romantic partner into their lives, or even think of somebody else in a romantic way. During the finale, the baker even asks the ghost of his wife (who's possibly only in his head), "How will I go about being a father with no one to mother my child?" (And this just after he and Cinderella agreed to live together with Jack and Red.) If it helps, take a look at the moment on video (it's a rather poor recording of a rather... odd... stage version, but I think it gets the basic points across if you just focus on the dialog).
Is it possible that Cinderella and the Baker develop feelings for each other while living together (after the musical ends)? Sure. It's possible, and neither the movie nor the stage musical definitively says that it won't happen. But that's not really what's going on at the point when Into the Woods ends - it's very much made out to be "survivors who bonded over a traumatic event (and have no other friendly faces to turn to) look to each other for support." Besides, it takes a whole lot more than living in the same house and taking care of the same kids to make people married. (By that logic, au pairs and live-in nannies are the husbands or wives of their employers.)