You may have to search a bit for the right contractor or engineer - sometimes I see one solution dominating in an area - "that is how we always do it" 

I don't have a solution but I think a real estate attorney or a title attorney would be a good person to talk to.

I paid off the loan as the solution.

Design happens to be one of my passions, and I’d love to help you brainstorm ideas or suggest some cost-effective design solutions that could work for your project.If you’d like, feel free to share some details about the style you’re aiming for or any preferences you have.

It most likely won't help them in this case but let's face it - they're not big on resolving their own problems especially when you're accommodating them.The longer you allow them to live rent-free with no solution in place, the longer they will do just that.

But my solution in your case would be to frame out a dividing wall of 2x4s and either drywall or if the basement is prone to taking on water then I’d look for something waterproof as opposed to the drywall.

Offer to buy them a few indoor portable heaters until you find a solution. 

I'm all about finding problems to solutions and figuring out how to make something work rather than simply conceding that it cannot work.

So the best solution is to buy a house needing extensive renovation for cheap and use that discount to change the layout when you bring it up to living standards. 

Invelo is a true all-in-one solution for real estate investors, built with industry-proven best practices.