Some states have what is known as a 'property tax cap rate' which guarantees the property taxes for a primary residence will not increase beyond a given amount by law. When a property is transferred via a quitclaim deed or a person is added / removed from the title, the 'capped value of the residence' is reset and the county may legally assess the property with a higher value, thus a higher property tax. Unfortunately, there is no way to avoid this issue while using an irrevocable trust outside removing one's property from the tax rolls and thus avoiding all property taxes legally (see Real Estate Secrets). Alternatively, the use of a revocable living trust can avoid any uncapping events and still maintain the ability for the home's transfer to avoid probate court.
NOTE: Be aware that the city, village, or township may offer a tax deferment for people over the age of 62. Provided that person's household income is not more than a specific amount, given the state.