In Lucas County (Toledo), we have a variety of jurisdictions that impose special assessments on the tax duplicate in addition to the real property taxes.
We have concluded that, unless there is a provision in law or a contractual arrangement that exempts a public entity from paying that particular assessment, it is owed by the land bank as it would be by any other property owner if the land bank continues to own the property after the end of the year it acquires the parcel. The prior special assessments, like the prior taxes, which may be delinquent are abated by the tax foreclosure judgment or the deed-in-lieu of tax foreclosure you receive. There may be the need for a statutory change that provides a continuing exemption, because I do not believe that we have one right now.
An example of the exempt by law: we have a Sanitary District (mosquito-sprayers) that imposes an assessment county-wide each year for their costs. The Sanitary District Revised Code provisions exempt a public entity from paying those costs, so the County Auditor voluntarily abates that assessment from our properties each year.
An example of the exempt by contract: we have entered into an agreement with the City of Toledo that exempts us from paying their regular special assessments for the time we own the property, except for bonded special improvements. So, a significant number of assessments are voluntarily abated each year by contract, except that we pull out those bonded improvements (usually sidewalks) and we pay the cost of that assessment like a regular taxpayer would.
An example of paying by agreement but not on the duplicate: we have entered into an agreement with our Solid Waste Management District for the $5 per year assessment they impose on all improved parcels. In lieu of paying it $5 a time on hundreds of parcels through the duplicate, we entered into an agreement where we pay it in one lump sum each year and then the assessment is voluntarily abated on the tax duplicate since it has been paid already. There is a provision of state law that authorizes that alternative payment arrangement.
All of this is to say that each assessment is different and can be tricky, but they probably need to paid or negotiated away.
This isn't legal advice and I would encourage you to seek legal advice and counsel as you need it in order to clarify these matters for the Clinton County Land Bank.