If a change in your situation affects whether you qualify for social housing and you don’t tell the Ministry of Social Development, you could be receiving social housing when you’re not entitled to it, or you could be paying less rent than you’re supposed to be. This could result in you owing a debt to MSD or in them investigating you for fraud.
MSD will investigate suspected fraud in relation to social housing in the same way as they investigate suspected benefit fraud (see “Trouble with Work and Income: Penalties, investigations and overpayments” in the chapter “Dealing with Work and Income”).