What damage will the fire monster and/or ghost do if left unchecked?

If you leave the disturbance without doing anything (they will last 10-15 minutes) more than once within a small timeframe a message will popup starting "your house has become vulnerable for 24 hours"

Now players can attack your house even when you are online. (Normally your house can only be attached when you're offline)

I've not noticed do any damage to my house as yet.