Loosing a pet is difficult and comes as a hard reality to your family members - including your pets. Though it is uncertain if pets understand the finality of another pets death it is well-documented that animals are capable of experiencing grief and loss of a family member.
Dogs and cats tend to see the family, including each other, as a unit and come to understand where their social position is in relation to the rest of the pack. When a 'pack' member dies, your animal may become uncertain of their role and how they fit in. You might begin to notice:
Changes in appetite;
Acting withdrawn or despondent;
Whining or howling in dogs;
Yowling or consistent crying in cats;
Pacing the home;
Hiding in dark spaces;
Changes in grooming or bathroom habits;
Close attachment habits;
Development of separation anxiety;
Not interested in playing.
Helping Your Grieving Pet Before/After you Euthanise the Other Pack Member:
Allow them to say their goodbyes with an activity they shared;
If feasible - euthanise your animal in your home and allow your animal(s) to come in and sniff them after the passing;
If you put your animal down at the veterinarians office - find a vet that is willing to allow your other animal to come so that they are able to sniff their pack member after they pass (Note: you will not want them in the room while they are being euthanised - due to complications that can arise during the euthanisation process);
Stay Positive - continue to talk to your remaining pets in a calm and upbeat voice;
Engage in new activities with your remaining pets - maybe start a new training with them or find a new game to play;
Continue Old Habits - continue the same routine you had before had to euthanise your animal;
Join a pet loss coping group on Facebook or through your vet.
The loss of a pet is a difficult time for your entire family. Each family member will cope within their own time - but remembering to provide comfort and support to your fur-babies during this time is aiding through the grieving process.