I recommend that you speak to a NY real estate attorney who can research your chain of title issues, and can advise you on your real estate options and potential liability.
Although it is the preferred procedure to record mortgage assignments, it is not always properly done. This does not necessarily mean that HFC is not the owner of your loan, and you should not be complacent and assume that this is the solution to the predicament you are in. It would be prudent to have an attorney review your loan documents as well as whatever documents were provided to you throughout the course of the foreclosure case.
Since you said that Saxon purchased Nova, Saxon would assume the obligations of Nova under a seperate agreement, and you would continue making payments to Saxon. This would not be a purchase of a note where an assignment would be required. When you say "reset" the loan, I believe you mean it was refinanced since you mentioned that HFC paid off Saxon. This means that Saxon is out of the picture and you had a new loan procured with HFC (unless you did a CEMA which is a consolidation). What you need to do is make certain HFC is the correct holder of the note, and there is no break in the Chain of Title. You have to carefully review the Complaint in your case to determine if there is proper standing. In any case, it should have been raised as an affirmative defense in your Answer. It is a very good idea to seek the advise of counsel in any foreclosure lawsuit where you are a defendant in jeopardy of losing your home- especially if you would like to keep the property.