Just because a bank holds your mortgage doesn't mean it owns your property. It doesn't matter if you're purchasing or refinancing. The mortgage holder only has the right to your property if you fail to pay back your obligations. Even then, it will have to go through a lengthy foreclosure process to take possession.
When you refinance your mortgage, you replace your existing loan with a new one. You will fill out an application and provide your financial information to the lender. If you will be using part or all of the funds to purchase a new property, you have to qualify for enough to pay your existing loan and to get enough cash out. This means you have to show enough income to support the new payment and all of your existing debt. Your property also has to be valuable enough that the refinance and cash out amounts do not exceed 80 percent of its appraised value. You will own the property, but the new lender will file a mortgage that will replace the old lender’s lien.
Assuming your cash-out provided enough funds to purchase the new property, you do not need an additional mortgage. You will own that home free and clear. Since you never pledged the new property as collateral to the refinance lender, it has no rights to it. If on the other hand you only have enough cash out to cover a down payment for the second property, and you need a new mortgage to cover the balance, you go through the application process just like before. It’s no different from the refinance in that you own the property, but the new lender will have a mortgage lien.
The mortgage lien is what secures the lender’s loan. When you close on a mortgage, whether it's a purchase or refinance, you sign a mortgage document describing the property, the lender’s interest in it and the amount you owe on the loan. The lender then records the document with the county clerk, so there is an official record that the property is collateral for the loan. Earlier liens take higher priority. This means if you refinance and then use those funds to purchase a new property two months down the line with a new mortgage, the refinance lender has first priority and the purchase lender has second.
While you initially keep possession of your property after a mortgage transaction, you can still lose it if you don’t pay the loan as agreed. After three to six months of non-payment, the lender will declare the loan in default. It will give you a brief window of time to bring the loan current or make alternate arrangements. If you can’t come to an agreement, it will list the property for sale. The lender will auction of the property for the amount you owe on the mortgage. If the bid is not met, the lender will take possession of the property as real estate owned, known in lending as REO. That is the only way a lender will end up owning your property.