Do you really think someone would pay for that?

There are two options for this.

1.The payment for this case was already included when the person was alive. In other words, the private protection agency was paid extra for promise to investigate death if their client dies.

2.Payments are made NOT on individual basis, but on group basis. Like the whole neighborhood signed collective contract with certain private protection agency and certain percentage is paid for possible murder cases. So in this case living members of the group will pay.

And most of all, even if he/she paid for that, how would he/she complains if it didn't happen?

Ideally due to reputation and publicity. Like if I discover that certain private protection agency broke its promise to investigate death of its client, then considering everything else equal, I won't use its services to protect my life.