How does a law enforcement handle a murder with the body already removed from the home?

If a person suspected a murder and informed the law enforcement. But, the body has already been moved before the law enforcement get to the home. Will the law enforcement still conduct a investigation or leave it alone. These criminals needs to be put in prison but law enforcement never can get them convicted without enough evident. These people kills every two years. And, it’s family members that they kills. Once they are reported, will the law enforcement keep a eye on them or what happen with this type of cases? Only serious people respond.
Thank you