Home Loan Services is a mortgage servicer; they, or someone else, will "service" your First Franklin mortgage pursuant to the terms of the mortgage and note that you signed. The terms to which you agreed in the note and mortgage stay the same. If you continue to pay there will be no issue. If you default, they can proceed with any of the options listed in the note and mortgage including foreclosure. 99% of the time, in the numerous changes of entity on a mortgage, there is a valid assignment from one to the next and things do not change. I can not even remember how many mortgage companies and servicers have come and gone on my mortgage on my own home.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
Companies don't just "go out of business," they sell their assets to another company or go bankrupt and their bankruptcy trustee appoints a receiver to take over their accounts. Your loan is one of their assets/accounts. Whoever inherits your loan, the new entity will take over the loan as they got it, and will enforce it as your loan documents with your previous/original lender allows them to, at the same interest rate 9or at a higher rate if the loan documents allow them to raise the rate, as in a construction/permanent loan).
If you don't pay the loan or come to some settlement with them if you've already defaulted on your 1st loan, then this lender may sue you to collect the debt. If you're sued, you need a lawyer to evaluate whether the debt is worth defending and if so, to defend you, or perhaps to file bankruptcy yourself if that's the best option.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.