Hi I purchased real estate in Michigan that was brought from the city quit claim deeds (previous owner didn't pay the taxes) a few months later I received bills for both deliquent water and property taxes from past years... does the city have a right to pass it onto me or should they have written off as a lost to them before auctioning it off.

You need to check the contract of sale. Most of the time, when property is sold because of delinquent taxes, the byer has to pay those taxes.

That would be because the tax sale for earlier tax years did not extinguish the tax liens for subsequent years.