That depends on when you are talking about. Animals were only really considered pets beginning in the 20th century the way we think of them. Licenses and having emotional connections to pets were considered childish in the 19th century in the western world but after WW1 Purina had a massive ad campaign that convinced people to take care of pets the way "they took care of your boys" abroad. So the emotional strings were being played through much of the 20th century.

In the Soviet Union, I suspect that the story is much different due to the bureaucratic and cultural norms of the era and region. However, the cultural norms were also different. I would venture to bet that pet culture as we know it today (i.e. the pet as a "family member") does not come until much later due to the agrarian nature of the Soviet economy. Obviously, this is a quick take but might get you started on how to find out more.

In the US, read Kathy Grier's "Pets in America" and Susan Johnson's "Valuing Animals." They have good bibliographies and will get you into a whole world of readings.