When i was little i was scared of people dying

When I was a kid, I thought about what would happen if a part of my family or someone I knew died. I got scared that if I thought about it too much, they would die because of me. I started making myself do the sort of things an OCD person does in order to keep my family from dying. They were completely pointless and unrelated tasks.

I know it isnt exactly normal to be like that, but I am curious as to whether anyone else felt scared/guilty like that as a child, or knows a child that does? I had a great life growing up so I know it does not stem from any sort of abuse.