Hud game

Those little Entity Claws represent the Obsession. If they're present at all, it means one of the players (Survivor or Killer) has brought an Obsession-based perk such as Decisive Strike or Save the Best for Last. Fun fact: The claws will wiggle when the Obsession is being chased by the Killer. So if you are not the Obsession and you see the claws start twitching, you now know the Killer is chasing them.

The one consistent thing, besides the chase twitches already noted, is Survivors get extra Survival points for being the Obession at the end of a match. 1,000 points if they die, 1,500 if they escape. From there it varies depending on the perk used. To offer some examples:

Survivor Perks:

Blood Pact: You and the Obsession see one another if either of you are injured and, if one of you heals the other, you get a running speed boost as long as you stay close to each other. Does not work if the user of the Perk is also the Obsession.

Object of Obsession: Increases the range at which you and the Killer can see one another when you are the Obsession.

Unique Wedding Ring (Key Add-On): Lets you see the Obsession's aura.

Most Survivor perks also increase or decrease the odds of your being the Obsession.

Killer Perks:

Dark Devotion: When you hit the Obsession with a basic attack, you become Undetectable for a time. During that period, the Survivor gets a Terror Radius.

Save the Best For Last: When you hit a non-Obsession with a basic attack, you gain tokens that speed up your recovery after landing hits. If you hit the Obsession with a basic attack, you lose tokens.

Rancor: Whenever a Generator is done, you briefly see everyone's positions on the map and the Obsession sees yours. When all Generators are completed, the Obsession becomes Exposed (downable in one-hit) and can be killed (Mori'd)

A more full list is here: https://deadbydaylight.fandom.com/wiki/Obsession