Hi there,
Unless your partner's ex has an interest in the land (or property) of the residence in question, she will not have a valid claim.
A caveat is merely a notice to the rest of the world, including all parties with present interest and all future parties looking to have an interest in the land, that there is a prior interest attached to the land, belonging to the caveator (your partner's ex in this case), that is not listed on the land's title. A person lodging the caveat does not need to show the validity of the caveat upon lodging. Once lodged, or at the time of lodging, you and/or your partner may dispute the lodgement. Where it is disputed, the validity of the caveat will be determined by the Registrar or court and will either be upheld or removed accordingly.
Once a caveat is attached to the property, it acts as an injunction so that the Land Titles Office will not be able to register any dealings related to the property unless the caveat is removed or the caveator gives consent.
In short, just because your partner's ex has an outstanding debt owing to her by your partner, if the debt is not related to the land in question, and if your partner's ex has not other interests in the caveated land, then the caveat will not be valid. If it is found that the caveat is invalid, then the caveator may be liable for penalty costs. This includes any pecuniary damage or loss suffered by any party with an interest in the land.