We have a house with a known foundation problem; an attempted fix was made that didn't work. So now, we have a house with a foundation problem that at least one fix didn't fix. Unknown is how much it would cost to fix the foundation problem.
The owner wants to list the property (if I understand the dynamic correctly) and is unsatisfied because it hasn't sold and/or the listing agent wants to drop the price some more.
Can the value of the property, as-is, be determined to a reasonable level of credibility? Yes, of course it can.
Does that level of credibility significantly depend on the reliability of a report to determine how much it will cost to fix? Absolutely.
You don't have that reliable report. Can an appraisal be done with that caveat and still conclude an as-is value? Yes; but there will have to be a lot of discussion on the limitations. Unfortunately, this appraisal is likely not helpful to the client in trying to determine how much they should sell the house for.
Here is what can be done for your client: Value the subject as-if the cost to fix the foundation is not feasible. In other words, the cost to fix is not recaptured in the market by the value of the site with its fixed improvement. Offer to provide the client with the value of the site as a development project. You will need a hypothetical condition (although I can imagine an extraordinary assumption could be used as well; I'd just use an HC because it is easier and cuts to the chase); and this would be appropriate given the problem to be solved (what are my pricing options for this property) and the fact that it is being done for purposes of reasonable analysis.
With this, the client will know how much the site is worth. With this, they can make a determination of where to list the property with all its warts and blemishes; if they receive a price higher than the site value, that means someone sees some value in the improvements even though no one knows for sure if the fix is feasible or not. They should take that offer. Otherwise, they should sell the property based on its land value. This provides them with meaningful information that they can use to evaluate the pricing recommendations of their agent.
Unless they provide the report necessary to determine feasibility and you are willing to do the work necessary to conclude an as-is value with that report, this would be a reasonable alternative.
Good luck!