But then there is something called improvements, and the improvements is just as much, making the assessed value $2x. she has no idea how this could be.

Your best approach is to show that the assessment isn’t supported by market data.

If you can't remedy it selling might be the only option or find a compatible tenant depending on the party level next door. 

I've read there's a structure that looks like:* HOA levies a special assessment, with a time limit (15-30 days) for a payoff.* Those that pay it off within the time limit are off the hook.* HOA gets a loan for the remainder, and only the non-paying units increase their HOA dues, or get hit with credit checks/collateral demands, or whatever else the loaning bank wants.* Special assessment has legal provisions that protect the paying units in all scenarios (e.g. in case of a default, the bank is only allowed to go after the personal property of the non-paying units).

Not enough data to do anything but blindly guess:(What were the previous special assessments for?

The investor buyer is purchasing the property from the Detroit Land Bank Authority (DLBA).As part of the closing, DLBA is requiring that the lender execute the attached Subordination Agreement.I don't love everything I'm reading, but I'm curious to see if others have gone through this.How did you assess the risk to the lender in this situation?

To more fully assess the situation, it'd be helpful to have the numbers in front of us with cash flow potential

HOA's scare me a little with the assessment fees and all the possible surprises.  

I then see people see them sell due to high assessments and HOA fees that they didn't see coming.

I'd love to talk to a local in the area who can help me assess neighborhood saftety, market potential over the next several years, and what I can reallistically expect for an ROI over the medium term (and, whether it would be a decent place to live in the interim!).