Sometimes a pet, is all that your parent might have to keep them company during those lonely nights at home. You know that you can't be there all the time and they know that too, so their pet becomes their trusted companion. So when they lose this pet, the loss can be as devastating as losing a loved one in the family. If your parent has recently lost their pet, you should try to do something to help them cope with this loss.
Make sure that you are them for them. Remember they can take this loss really hard and they may quickly become depressed and feel like part of them died with their pet. Be there to remind them it's OK to grieve for their pet but to reassure them that everything is going to be alright.
Consider inviting your parent out to lunch or to come over and spend some time with the family and have dinner and watch a movie or play some games. You need to make sure that your parent still feels loved and needed. Remember they feel like they just lost all of that when their pet died.
There are pet loss support groups and hotlines. Do research on this and give these groups names and numbers to your parent. If your parent is reluctant to go to a meeting alone then offer to go with them the first time they decide to go to a meeting. Let them find out with you there that they are not the only ones feeling the way they are.
Although another animal is not going to completely take the place of the one they loved so dearly it is a good idea if you ask them if they would like a new pet. If they act as if they could never have another one then you might take them for a visit to the local pet store or animal shelter just to have them exposed to the animals and see how they react. It probably won't take long for them to spot one that catches their eye and they want to bring it home with them.
Make sure that you are there to listen to your parent when they try to express their sadness about losing their beloved pet companion. Don't act like it's something silly, show you are concerned and that you truly understand. Put yourself in their place and wonder how you would feel if your own dog had suddenly died.
Ask your parent if there is anything around the house that you might be able to do for them. See if they need to have you do some of the yard work or go shopping with them. Ask them if they want to go out to a movie or if they would like to have their hair done or go for a walk. Whatever you can do to help them get through their grieving process is going to be beneficial.
Whatever you do through all of this, remember to show compassion.