They can do this. Who knows why they did it this way, but the same outcome will happen either way. You can't be evicted until after foreclosure, so I am assuming it already happened. If you have any doubts, contact a local attorney who handles foreclosure defense.
Everything you said the bank did is possible and legal - with the possible exception of the "no knowledge" part. You should have been properly sent a notice of default and intent to accelerate and notice of sale/acceleration with regard to the home improvement loan. If these things did not happen and if the home was not actually sold/foreclosed at the auction, this series of events could be legally actionable as a wrongful foreclosure. It does sound like your home was foreclosed since you mentioned the title changed.
Banks don't always foreclose when they have the ability to do so. There is no such thing as an "obligation to foreclose". I have seen this before when property values are so low the bank does not want to deal with costly possession and maintenance. That said, it is perfectly acceptable for the bank to transfer its rights to other parties allowing them standing to foreclose.
This general opinion DOES NOT create an attorney-client relationship. No communication can ever replace the specific advice of a lawyer. Each person's situation is different, and additional facts can change legal outcomes. You should consult privately with a lawyer if you have a question about a legal dispute.