My question is -- will the Estate be liable
for any "loss" that incurred by selling the
car to my brother for less than the loan
Absolutely, positively, yes.
The estate owes the entire balance. The estate will have to make up the difference whether you sell it or turn it back to the lender.
Otherwise, the finance company will just not release the lien and is likely to repo the car if there is a default. Or will sue the estate for the balance and the money will have to come out of other assets.
Or, a similar scenario - if I turn the car
back over to them and they sell it at an
auction for less than the loan balance, can
they make a claim to the Estate for the loss?
And you, as executor, have a fiduciary obligation to act in the best interests of the estate, not the best interests of your brother.
So if you mess up on the car deal, the remaining unpaid balance could come out of your pocket if another heir litigates against you for malfeasance.
Be very careful how you handle this.