So, I was thinking that maybe somehow Tadashi survived the fire. Do, he possibly got locked in a certain room that wasn't on fire. Then, if firefighters came to put out the fire and noticed there was still a living person, they could have called an ambulance.
Afterwards, the ambulance took Tadashi to the hospital but no one found out that he is still living. Maybe, if they make a second movie, Hiro, Gogo, Wasabi, Fred, and Honey Lemon learned that Tadashi is still liking when they get called. Or, so you know how Baymax showed Hiro the clips of Tadashi showing the clips of Tadashi trying to get Baymax to work? Well, Baymax scanned Tadashi so the group can track down Tadashi and find out he is still living. Tadashi may then be very satisfied that Baymax worked and helped out MANY people.
Or maybe the one who went to jail in the end (I can't remember his name) got out of jail and told Hiro that Tadashi is still living. That is my theory!