The core of "Finch" is the foregone conclusion of its protagonist's death. The entire narrative is a preparation for this event. Finch is suffering from radiation poisoning, a fact that becomes more apparent as he coughs up blood and his condition worsens during the journey. In a moment of respite where they find a location with safe UV levels, Finch has a final, meaningful day with Jeff and Goodyear. He dons a white suit he'd saved to meet his estranged father and finally succeeds in teaching Jeff how to play fetch with Goodyear, a crucial moment symbolizing the dog's acceptance of his new guardian. This allows Finch to die in peace inside the RV, knowing his mission is complete.
Following Finch's death, Jeff gives him a Viking-style funeral pyre, an idea Finch had mentioned earlier. Now truly on his own, Jeff steps up to his responsibilities, using a built-in can opener Finch had secretly installed in him to feed Goodyear, a poignant revelation of Finch's foresight. Jeff and Goodyear complete the journey to the Golden Gate Bridge. They find it not as a bastion of civilization, but overgrown with plant life, a sign of nature's recovery. More importantly, they discover messages and notes left by other human survivors, indicating a community nearby. Having been taught by Finch to be wary of other humans, Jeff makes his first truly independent decision, choosing hope and community over fear. He pins Finch's postcard, now with a drawing of the three of them, to the bridge and heads off with Goodyear to find the other survivors, bringing Finch's legacy of hope and connection full circle.