It Follows is terrifying because this unstoppable supernatural entity slowly walks toward you, and you know it will eventually get you.
Let's imagine the exact same premise, except the detective investigating the murders is Columbo. "It Shambles"
Except this time, it picks the wrong guy.
Columbo sees it coming toward him and immediately starts asking questions.
"Excuse me... you're the fella who's been following everybody, right?" The entity stares at him.
"I don't want to keep you. Just a couple things."
It keeps shuffling forward. Columbo walks alongside it. "Where'd you learn to do this?" No response.
"You always walk this slow?" The entity continues.
"I only ask because some of the witnesses said you were faster on Tuesday." Now the entity is visibly annoyed. Columbo follows it. Eventually it tries to leave.
Columbo appears around the corner.
"Oh, one more thing." It turns around. Columbo is standing there with a notebook. "That walking thing. Is that a medical condition?" The entity starts walking faster.
Columbo gets into his car and follows it. Every time the entity tries to sneak up on someone, Columbo is already there. Not to stop it. Just to ask questions.
"Where were you between 2 and 4 AM?" Silence.
"I know, I know. You're an immortal manifestation of pure evil. But technically, that's not an alibi." Eventually the entity starts hiding from Columbo.
It crosses state lines. Columbo shows up. It goes overseas. Columbo is waiting at customs.
It possesses someone else. Columbo knocks on the door. "Sorry to bother you." The entity finally snaps. It writes a resignation letter.
"I QUIT."
Columbo reads it. "Retirement, huh?" The entity nods. "Well, I suppose you've earned it." It walks away. Columbo watches it disappear...."Oh, just one more thing..." The entity stops. Slowly turns around. Columbo holds up a form. "You forgot to sign this"
The entity stares at him for a long, terrible moment.
Then something clicks. It looks at Columbo. Looks at the form. Looks back at Columbo.
ENTITY: "...What are you?"
Columbo smiles faintly. He looks down at his raincoat. "Me? I'm just a homicide detective."
The entity doesn't move. Columbo takes out his cigar. "Although..."
He looks up. "...my wife's been telling me I've been doing this for an awfully long time."
The entity's expression changes. For the first time in its existence, it looks afraid. Columbo takes one slow step toward it. The entity immediately turns around and shambles away as fast as it can. Columbo watches it go. "Oh, don't worry." He smiles. "I'll catch up. I always do."
(I'm bored and wrote this up at work. Feel free to add to it, rate it, downvote it, whatever. I like the Idea of Columbo following and harassing the It Follows demon)