MMCA Mitsubishi Motors Credit America Trying to collect after death... Schaumburg, Illinois

I do understand how auto financing works. I also understand that as co-signer I am responsible for the balance owed.

First of all sorry about your aunt, but there are some things you don't quite understand about auto financing.

If you co-sign for a loan, that means you are making a legal agreement that you are EQUALLY responsible for the loan.  In the even that the primary borrower can not pay(for what ever reason), you are required to.

When the car was reposessed they sell the car at auction and the borrowers(you and your aunt) are still responsible for the loan balance.  Unless this debt was taken care of from her Estate when your aunt died, the loan becomes your sole responsibility.  So yes they do have a legal right to come after you for the deficency balance, that is up until the Statute of Limitations expires. 

This is no different than any other finance company or lender would be.

Now, this is independent of the collection activities.  Your caregiver did the correct thing in calling 911.  If they actually attempted to enter the home, hopefully criminal charges against them was pursued.

If MMCA is a 3rd Party Collection Agency you have rights under the Fair Debt Collection Practices Act.  One of those is to request that they stop contacting you.  You can do this by sending them a "Cease Communications" letter by certified mail with return receipt.  Once they receive that they can not contact you to attempt to collect the debt.  But they are still allowed to take further action, such as filing a suit against you.

"MMCA continues to contact me almost daily demanding I pay over $10,000 for a reposesed car with a deceased owner"

  Sleazy collection tactics aside, you may still be on the hook for the balance of the lease (and accumulated interest and fees).   As a co-signer, you're responsible for the balance if the primary on the contract cannot make the payments.