Think back to all of your closing where only one spouse (typically the wife because we men just hate to pay our bills on time) has enough credit to qualify for the loan. The (husband) has to sign a document (Mortgage) that when recorded lets the public know he is aware of the note on the property.
Now if one were to refinance, using traditional means, then the same would apply. In some cases, a private lender will hold a small note and not record it, but that is not as likely to happen these days.
I am certainly glad that Brian opnied on this answer, because there is bad info out there.
Please don't be ofended by my response, but please...PLEASE pay close attention at your closings.
If you are on the deed of the house, you would have to sign off on any mortgages put on the property. You would not have to sign any Notes. Therefore, at a closing, you would have to sign the mortgage only (maybe a few other docs).
You sign the actual mortgage of the property because you have a 1/2 interest in the house. They need you to sign because if you don't, and then the house went into foreclosure, they would not be able to foreclose on your 1/2 interest in the house.
If someone refinances and you don't sign a mortgage, then they have only mortgaged that other person's 1/2 interest in the property. Bad for the bank! If it ever went into foreclosure, they would not be able to sell the property to satisfy thier debt, as your 1/2 interest is not mortgaged.
The long and short of it is, you would have to sign any mortgages, but not any financing documents such as notes, which affect your credit.
If you're not on the mortgage, I'm not sure you'd be notified. However, there probably are instances--state by state--in which partners or husband and wife both might be required to be notified, even if both aren't on the deed. Again, I'm not sure; you have to check.
As for a co-signer being added to the deed--again, I'm not a lawyer--but the deed and the mortgage are two different items. However, it depends on how the property is held--tenants in common versus tenants in the entirety, for instance. With tenants in common, the other person could sell or assign his interest in the property to someone else. So, and I'm just guessing here, if your ex-hubby is interested in refinancing the property and pulling some money out and his current wife/partner is going to be co-signing, it could get very complicated. So...as already said...check with a good real estate lawyer.
Having said that I would not be suprised if it was overlooked. You can check the registry of deeds for mortgages.