The risks from having a house in a negative pressure include increased higher utility costs, poor indoor air quality, increased risk of mold building up inside the wall and in extreme cases can lead to asphyxiation from smoke or carbon monoxide backdrafting down the chimneys.
For example, if someone were to use their fireplace and range hood, there could be risk of asphyxiation if there were no protections against depressurization. When the range hood is turned on, the chimney becomes that path of least resistance for replacement air when the house is drawn into a depressurized state. It takes literally seconds to bring smoke or even flames back into a house when a fire is burning.
Even if your house does not include a spillage susceptible combustion appliance, the outside air would be pulled inside through the various leaks in your building envelope. In winter, the cold outside air can condense inside your walls where it changes state. This can and does lead to a long-term mold issue possible structural integrity issues like rotting wood.
Managing depressurization is done by installing a make-up air (MUA) system, which provides replacement air from the large exhaust devices at the time they are used, keeping the indoor and outdoor pressure balanced. While this resolves the complications of depressurization, bringing in unconditioned air from the outside will raise your heating and cooling bills, not to mention the cost of the make-up air system in the first place.
In order to properly size a make-up air system, we can perform an HRAI W-3 calculation to manage depressurization in your home.