If a property has a mortgage and 2 people are on all the original documents can 1 individual transfer his rights by quit claim deed to another individual that is not on the mortgage or original documentation, by form of a quit claim deed and a financial arrangement.
There are a couple of parts to your question, let's see if we can help you sort them out. But as a general caveat this web site won't give specific information or advice on any particular state laws, just general advice. Mortgages and deeds are really local issues so be careful applying the general advice below to your state.
"If a property has a mortgage and 2 people are on all the original documents" - we assume this means the same two people bought the property and signed the mortgage. If its a husband and wife the result might be different. We will assume not.
"...can 1 individual transfer his rights by quit claim deed to another individual that is not on the mortgage or original documentation..." Whoa partner, before you transfer anything that there is a mortgage on you had best read the mortgage. Most mortgages won't permit any transfer without the lender's approval. For some basic background, when you borrowed the money you probably both signed a "Note" to the bank. This is a legal document in which you each personally guaranteed the amount borrowed would be repaid. This note or loan document likely has terms (requirements/restrictions) you need to review before transfering the property. The lender then secures their ability to get repaid by getting a lien on the property. The document that does this is a mortgage, which is then recorded in the public record to be sure that no one can transfer the property without seeing the lien/mortgage exists. Now one more piece of background. Anyone buying or otherwise receiving real estate should get title insurance to assure that they have good ownership of the property. The transferee, the person you want to quit claim to, won't be able to get this without the mortgage being addressed (or the mortgage will be an exception). You had best talk to a real estate attorney in the area where the property is located about these issues.
".... by form of a quit claim deed and a financial arrangement..." A quit claim deed just says that the transferor is giving the transferee whatever legal rights the transferor has. If I were getting an interest in real property I'd want a "stronger" deed. In some areas this might be called a "bargain and sale deed with covenants against grantor's acts", etc. The transferee should want good title.
The bottom line is that the transfer is only giving the trasnferee what the transferor has, and likely the transfer will trigger the mortgage being due. If the current interest rates are lower, and there is no prepayment penalty you might want to make the transfer and refinance.
Lots of issues, but hopefully, with the sketchy facts the above will get you on the path you need.
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