One of the advantages that dogs have over people is that it is legal for them to be euthanized.
When they can't bear to see Karenin suffer anymore, Tomas and Tereza decide to put him down.
Because Tomas is a doctor, he takes responsibility for doing it himself.
Tereza can't stand the look in Karenin's face, "a look of awful, unbearable trust" (7.5.6). His look was a question, because in Karenin's life, Tereza is his whole source of truth. Tereza knows that no one will ever look at her that way again.
They usually don't feed Karenin sweets, but now Tereza puts a few pieces of chocolate on the floor before him. He doesn't raise his head.
Tereza lays down on the floor and he licks her.
She goes out to tend to her cows, and when she comes back Karenin is still lying on the floor in pain.
When Tomas comes home, they pick up Karenin and lie him on the couch.
Tomas cuts away the fur over a vein and while Tereza talks to the dog soothingly, Tomas injects the needle.
Afterwards, both Tomas and Tereza have to go to work. They leave Karenin's body on the couch.
When they come back, Tomas begins to dig the grave in the garden. Tereza leans over Karenin and mistakes her own breathing for that of the dog. She thinks he is still alive, but Tomas assures her he is not.
They bury him in the garden along with his leash, collar, and the chocolate Tereza tried to feed him earlier.
Tereza remembers her dream and imagines a monument above the grave with the words, "Here lies Karenin. He gave birth to two rolls and a bee" (7.5.32).