To see a pet in your dream represents civilized instincts. You are keeping your temper in line. Alternatively, seeing a pet indicates a need for love and acceptance. Perhaps, you are lacking attention from others and are feeling neglected. The pet may also be a pun for “petting” as in some sexual behavior.
To dream of a dead pet suggests that something that you had thought was left in the past is coming back to haunt you. Similarly to seeing your childhood home, a past pet serves the same function as trying to bring you back into that particular time period. A situation in your waking life may parallel a situation from your past and the dream is providing a means of resolving it.
Dreaming that your pet escaped or got loose implies that you need to express some of your primal urges. You can not suppress them any longer.