At the time of origination, residential mortgages will have limits on the equity-debt ratio. If you fall below a certain threshold (e.g. sub-20% downpayment) your lender may require you to carry private mortgage insurance (PMI). If your home's value were to fall substantially, your equity-debt ratio could be pushed below the threshold -- e.g. if tax assessments were updated.

I've never heard of situations that have re-triggered PMI... but it doesn't seem outside the realm of possibility.