Yes, it is my understanding the first mortgage can foreclose even if the property has one of these loans in a subordinate position. And if the first forecloses, these loans will have their security interest in the property wiped out. They may be able to pursue the former owner to collect the unpaid debt, but not the buyer at auction.
As for whether or not it is a “below market rate house,” the only thing that matters is whether or not there is a deed restriction limiting the resale of the property to certain parties. If you are concerned about that you should carefully review title. If the restriction was recorded after the foreclosing loan, it too should be wiped out by the foreclosure.