Homeowners in Michigan must pay property tax each year, to the local taxing authorities. In most Michigan counties, the tax is due in two installments on July 1 and December 1, though specific counties may have different due dates. 

You actually have three years to repay missed property taxes before your home is foreclosed on. It's best to pay those taxes back a soon as possible, though. The longer they go unpaid, the more fees and interest will accrue, making it more expensive to repay those taxes. 

Property Tax Exemption:
 

Pursuant to MCL 211.7u, eligible low-income homeowners may apply for an exemption from property taxes. An eligible person must own and occupy his/her home as a principal residence (homestead) and meet poverty income standards.