I think they are running away from the feeling of emptiness inside from being alone. It means nothing to them literally in that sense. That is why people pursue it, as you say. Because it can only be a source of meaning for you when and while you have it.
It shouldn't be a major factor in your life other than when you have it to my mind. Because that would be living in denial of your current situation. It doesn't even require the object of your love has to be alive, but the feelings of love still need to be alive. When even those feelings are not alive, love can quite easily come to mean nothing to you, as it is a purely subjectively felt thing. I don't think many people face this latter situation for very long if at all in their lives, as they quite wisely move from one relationship situation of love to another as a replacement. Certainly I think this applies to love with a sexual element anyway. Love, like nature, abhors a vacuum.
I was just trying to highlight the paradox of its subjective significance as a force in our lives.