If a Minudeh (excommunicated individual) dies, does his or her family sit shiva for them? Does it matter whether they previously mourned this individual as part of the excommunication process?
See ShA YD 334:3-4 and 345:4. In short, if the Niddui was due to monetary issues, they would sit Shiva, but if it was due to Issurim (heresy, not listening to the Rabbis, etc.) then they would only sit Shiva if the one in Niddui had repented (even if he wasn't yet formally released from his Niddui). No matter what they can accept condolences, just like the relative of one who consciously kills himself (345:1).