IF you paid CASH for property and own it, but have a mortgage for the house that sits on the "paid for in cash land", what happens if the home is foreclosed? If the mortgage company just owns the house and not the property it sits on, what happens in a foreclosure?
This is a great question and while I can't give you an answer that applies to your specific situation I can give you some general information about mortgages and how loans are secured that you may find helpful. Some of the terms that you want to be familiar with is chattel, real estate, and fixture.
A mobile home that is not permanently affixed to the land is chattel. A mobile home loan has the mobile home as security and the title to the mobile home reflects that it is security for the loan just like an automobile. If the owner doesn't make the payments, the lender repossesses the mobile home. Whether the owner owns the land or rents the land the mobile home is on doesn't matter. If the owner had paid cash for the land, they still own that land. In this case the mobile home loan is not a mortgage. The security for the loan is the mobile home and the lender can physically remove the collateral (chattel) in the case of the buyer's default.
When you buy a home that is constructed or "affixed" to real estate, you actually don't "buy" the home, you buy the real estate. The home is a "fixture" of the real estate. When a lender makes a loan on real estate the security for the loan is the real estate and that includes any improvements or fixtures of the real estate. In almost all instances, that includes improvements made after the loan is made. So if someone buys a home with a mortgage loan and later makes an improvement like adding a bathroom, then defaults on the loan, their interest in the real estate is foreclosed upon. They lose their ownership of the home, including the bathroom they added.
If someone pays cash for property and then borrows money to build a home (or permanently affix a mobile home), the owner gives the real estate as security for the loan. The owner may still own the land, but they no longer own it "free and clear." The lender has a lien on the real estate (the land) and all of the improvements or fixtures on the land (the house). If the owner defaults on the loan, the lender forecloses on the owner's interest in the land and then sells the property to recover as much of the loan as possible.
So after a lender forecloses on a defaulted mortgage loan used to construct a home, the lender never "just owns the house and not the property if sits on." The lender owns the real estate the home is on. Otherwise how could the lender recover the security for the loan? A lender can not remove from land they do not own a house that is permanently affixed to that land in an attempt to recover its losses. Imagine how impractical that would be, not to speak of the legal implications.
You should speak with a knowledgeable real estate attorney if you are not sure whether your home is chattel or an improvement, or if you are not certain whether you gave an interest in your property as security for the loan on the home.