The first kind of infinite problem is the problem of a house that was built on a non-conforming lot. “Non-conforming” is a fancy way of saying, “so out of code it isn’t even funny.” (Well, not really, but I had to say it!)
“Non-conforming” really means the lot does not meet the code, even if it is by a little bit. If the house is on a grossly non-conforming lot, the house can’t be changed much and still be allowed to be there.
So you see the problem when you want to modify a nasty little house built behind another house. It is an unsolvable problem, even with a lot of money. The same is so for a tiny house stuck on a tiny lot in a big house and big lot neighborhood.
The other unsolvable problem is when the land is not fit for a house, but a house is there. I see this once in a while.
My client declined to buy this house. Why? Because the pillars were only there a year, so my client couldn’t be sure the fix would work. Even though the seller’s engineer thought this would work, there was another engineer who thought the new back foundation and deeper footings would work years before. My client bought on more solid ground.
I saw a similar problem with a house built on peat. Peat is the soft soil that develops in bogs. It is a dumb thing to build a house on it.
One of my clients saw a house built on peat. The seller had information about how the front foundation wall was totally rebuilt ten years before. The floors seemed straight, everything inside seemed fine. That was until the inspector found a big, displaced crack in the foundation. The poor house was still sinking. My client beat feet out of there.