My team is looking to update some of the content in the emails that are a part of our nurture program. If we update the content, will people who have exhausted the program receive the emails if they aren't technically "new" just the content has been changed?
No, people won't receive the same email again from the EP. Engagement program references the stream content by their id and not by the content itself, hence updates to the content of the email would not make people receive it again from an EP.
Agreed with @Darshil_Shah1's comment. The exhausted leads will not receive the updated emails as they already have received the same, however if you create a new email with the updated content and add that to the stream then all the leads in that stream will receive the content.