She better hope they have done it.
It doesn’t really matter. She’s going to lose the house either way. I’ve never heard of a property tax-collecting jurisdiction doing anything beyond seizing the property. In a foreclosure, the mortgage-holder becomes the legal owner of the property and thus responsible for any unpaid taxes. As part of the transfer of legal ownership, the mortgage-holder will have to pay any back taxes. If they’re stupid enough to refuse to do this, then the ownership won’t be transferred, and the property would be seized directly from the current legal owner (i.e. this woman) by the tax-collecting jurisdiction and auctioned off to satisfy the tax lien.