Marking, that's the name for them for the sign contained in their gulp. When an Alpha has marked his Mate, the Omega will live depending on the Alpha. But they can also decide on each other's signs, but that can damage their emotions.
Usually, they call it rejecting or breaking the relationship as a pair of Mates. But breaking a relationship can be fatal, an Alpha or Omega can die. But most often Omega always gets fatal consequences. Even many Omegas die after a few days of being rejected by their Alphas.
Like what happened between Jason and Stella. The Omega dies, unlike the Alpha who can still live despite feeling a huge sense of guilt. But in Caroline's case, it's different, having two statuses makes her a little special. Even having the Mate mark wasn't a bad thing for him.