The paper bag strikes me as an almost biblical reference. In the beginning stories of the Redeemer, Jesus, he was born in a manger, which is a place where animals eat
(to eat=manger). And then on his last evening on earth, he took bread and presented it to his disciples and said, "Here is my body, which is broken for you."
In the same way, Ennis arrived at Brokeback Mountain with a couple of shirts in a paper bag. At the end of the movie, he was leaving Lightning Flat, with the two shirts, consecrated with blood, in a paper bag.