It is not known how Darnel survives on his own. As the pathway to the 2nd floor of his shop is not barricaded, zombie hordes can swarm in with ease, and if the players search his cupboard, they will find that he has no food stored there. In fact, the floor that Darnel is on can be a potential horde attack location, with zombies falling from the roof.
However, it can be assumed that since Darnel is a war-hardened veteran, survival is not a big problem for him. It is likely he goes out scavenging for supplies in his free time, or that he hides out somewhere else, and is just at his shop to use the workbench there. It is possible the players have simply encountered him when he was not out scavenging or at his hideaway during their visit to Brookvale.
Zombies will not spawn on the second floor, but they do enter if a horde attack is going on.