Unfortunately, Hroggar's wife and daughter, Helgi, perished in the blaze. When asked about the burned down house, the Jarl will indicate that the house had once belonged to Hroggar, and that one night the house had burned down while he was away. Who am I to gainsay them?' ― Idgrod Ravencrone

'Hroggar's house fire? He lost his wife and daughter in the blaze. Note that the Dragonborn may have to 'enter' the burned down house in order for the innkeeper to have the dialogue option to speak with the Jarl. Initiating the quest through Jonna, the guards, or the Legate, will all result in the first objective being to speak with the Jarl anyway. The Dragonborn may also speak to any of the guards in Morthal to initiate the quest, as well as the Imperial Legate inside of Highmoon Hall. Alternatively, Idgrod Ravencrone (or Sorli the Builder if the Dragonborn sided with the Stormcloaks during the Civil War) can be asked regarding the subject. This quest can be started by speaking with the Moorside Inn innkeeper, Jonna, who will mention the burned down house nearby. Hroggar took Alva as a lover immediately after the fire, and many in town think he did it.

A mysterious fire killed Hroggar's wife and child.

Where to find helgi after dark