From your facts, your partner has the same title interest as you. Evidently, she is also on the mortgage and note and wants to be clear of that obligation. Without knowing the terms of your mortgage, I would assume that today's interest rates are lower than what you are currently paying. Another consideration is how much money was contributed by both of you in the 2009 purchase. Right now, you have all of the rights and obligations as the sole tenant to the property - and she is an owner and obligor without any possession or rights - even if voluntary. Assuming you two did not have any kind of agreement specifying your rights as "partners" in the property, it is best to work together to sever your ownership rights in the property completely and fully for both of your benefit. If not, she has the right to file the partition action to free herself from the property obligations.
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The problem that she has is that she is still responsible for that debt, even though she has moved on. That is likely to remain a problem for her. A partition action will be a problem for both of you, mostly because of the legal fees that you are both likely to waste, AND she will likely still be responsible for the debt because the bank is not going to want to let either of you off of the hook for the responsibility for payment, especially if there is no equity in the property. If you were married and tried to do what she wants to do the bank wouldn't remove her from the note.
You should talk with a lawyer who knows what they are doing in this area of the law. Someone who can talk with both of you, or both of you and her attorney if she is already represented by counsel (sounds like she might be if she knows about the concept of partition) to try to come to an amicable resolution that doesn't cost your both a bundle of money.