I agree with Livin in Sim, it does border a mental health issue. Extreme possessiveness usually surfaces under the duress of negative experiences. People can feel completely overwhelmed when met with such a strong emotion they (perhaps) did not know they could possess. Through life-experience and better understanding of what has happened, people no longer deal as much with the sharper edges anymore.
People don't stay the same in their lives. I hope for the future generation of the Sims franchise, these emotions will have the ability to be refined/transmuted through life experience. So, an elder may offer advice and solace to a younger adult or a teen who may endure similar trials and tribulations. A child would have the potential to grow, but in the end, life may dictate more strongly where they'll end up.
I really do like this trait, however and have given it to a couple of simmies. My jealous sim is head-over-heels with a non-commital townie.
