This is an interesting question. First, define “obsessed.”
Many people read the obituary section of their newspaper every day. We wouldn’t call that an obsession, just an interest and curiosity about the members of their community.
We’re not particularly sure what you’d have to do to be defined as “obsessed with obituaries” but if you Google it, there are several articles about people who apparently have a fascination with reading them.
If you need to write an obituary for a loved one, our Obituary Writing page or Obit Kit can help you out.