This question is a real problem that many children will face, when one of the two parents suddenly left, then how the other one should continue to live on?
First, take your mother out for a walk.
If the father died, then the mother must be in a very painful and lost mood, at this time as a child should be more accompanied by their mother. Take your mom for a walk in the park, or take her for a short trip on the weekend, so that she can see a different world outside and change her mood.
Secondly, develop new hobbies.
Then you should also cultivate your mom's new hobbies in your life. For example, you can take her to learn square dancing, or some of the things she is more interested in. Only if she has new hobbies, then she won't keep thinking about those painful things. It helps to distract her attention and relieve her painful lost mood.
After my colleague's father passed away, my colleague saw that my mother was lonely and was always alone with her tears, so she enrolled my mother in a modeling team for the elderly, because my mother is tall and always pays attention to how she dresses. When mom found happiness inside this group, her whole body was no longer depressed and she was very energetic all day long.
Again, help her make new friends.
Then to help her make new friends, you can take your mom to join some senior citizen clubs, or enroll her in a travel agency that specializes in the elderly. The new friends will be able to talk and laugh together, which will also help to alleviate her frustration.
More often than not, when one of your parents leaves first, the other one will be in great pain. The most important thing that a child should do is to be there for him/her and to help him/her regain confidence in life.