The thing that separates the infected in “The Last of Us” from the regular zombies you know and love, is that the infected can’t live forever. They are not reanimated dead that rise from the grave, but people kept alive by the Cordyceps infection. Eventually, all infected die. The problem is that, even if the host body can die, the infection doesn’t — it just spreads.
After the host dies, the fungus eventually exits the body, which often causes the former host to stick to the wall or floor. This is most common with stalkers, given how little they move. In all cases, however, Cordyceps festers until it fully consumes its host and then spreads throughout the environment via tendrils and vines. This is part of why this franchise rules — it is more than just supernatural ghouls or extreme rabies, it is a very real infection blown out of proportion, using actual science to dig deep into our nightmares and sow them right back to us.