The death is not shown on screen. The dog has cancer and is given a catheter and weeks to live. In the next scene, the owner and dog are lying down, and he removes the dog's cone to give her some scritches. He falls asleep, and there's some suspense while she licks the catheter tubing, but ultimately he wakes up and puts the cone back on before any damage is done to the catheter. After, a phone message plays requesting the owner to pick up the dog's remains. There's a short memory sequence depicting the dog as the owner cries about missing her. You won't miss much if you need to fast forward through these scenes.