Lease Finance Group, LLC Lifetime charge of credit card terminal?? Do my heirs inherit this? Chicago, Illinois

I leased a credit card terminal through the Lease Finance Group, LLC for my business.  After 25 years of owing a retail tire business, I was ready to sell my business and retire.  When I called Lease Finance Group and told them that I was selling my business and would no longer be needing this machine, they informed me that they would provide a box for me to return such and everything would be taken care, and even thanked me for my loyal service and prompt payments.

Needless to say, I never received a box for the return of the terminal, even after calling this business periodically to inquire about such.  I returned the machine in my own box and assumed that this would be all that was required since I would no longer have any need for a credit card terminal for a business that was no longer in existence or at my home, since I was retiring.

Lease Finance Group continued to take payments out of this business account and when the funds from the sale of the business were disbursed, I was written a very nasty letter stating that they no longer could draft this account and that I owed them for the previous month and current month's billing.  I called them yet again to tell them that this machine was returned and that the business was no longer in existence.

This company then started drafting out of my personal account.  I do not know how they even got my account number.  Luckily I live in a small town and my bank caught this and called and informed me of such.  My bank blocked any future drafting of payments from this company.  I talked to an attorney and they sent a letter to Lease Finance Group stating to immediately cease any further drafting from my account or any future correspondence. 

I have now received a Notice of Acquisition and Demand for Payment letter from Pushpin Holdings,LLC that they have bought previous lease agreements from Lease Finance Group and demanded that I pay the sum of $1,315.40!  This is ludicrous!  I wonder if when I pass away, will my heirs inherit this debt?