This is a little complicated butthe general rule is that partners cannot sue one another. they must first dissolve the partnership then if suit is appropriate they are free to go ahead.
First you have to look to the terms of your partnership or operating agreement. Assuming that it is all 50/50, then you do have a right to make a claim for contribution if you end up having to pay more than 50% of the company debt. The problem is, you usually have to make a disproportionate payment towards a debt before you have the right to make the legal claim for it. I recently answered a partnership question where one partner wanted out, and the issue was whether the departing partner was entitled to be bought out. Take a snapshot of the assests and debts, and value the business as a going concern, and also as if it were being disolved. In this case, it appears that there may not be a posative value. If you are willing to continue the business, you should be asking the partner that is leaving for payment, before you let her out of the partnership. If you are not willing to continue it, at the very least, you should ask for a promissory note, for half the debt less the value of her share of the assets going to you. That is what you would be entitled to, if she could pay it. The promissory note would just settle the amount due. You should also seek to have the promissory note secured by a mortgage on the the home, combined with a due on sale provision. That way when it sells, you will be paid. Even if she won't agree to that, it would be easier to make a legal claim on the promissory note, than on the partnership, because the amount due would be already agreed upon. Of course, she could file bankruptcy and any unsecured debt or cleim would be discharged.