Developing the capacity to have an inner happiness helps us to not be so dependent on them for our happiness. Developing more unselfish emotions and insight into the 3rd characteristic, that they are not really "mine". Often we have this idea that if they are ours, then we should be able to control them and prevent them from dying because they are "mine", but nothing in this world is really ours. Doing a type of death reflection where we go back 100 years can help, seeing how even though everybody loved each other at that time, they couldn't hold onto them - they all died. Going into the future, seeing the universality of death helps us to loosen our attachment a little, because we understand that coming together for a short time is all we can do.
Also, developing more Compassion/Lovingkindness and Equanimity, these Brahma Viharas, reflecting that they are the owner of their own Kamma and we are the owner of ours. So it is actually just continuing a lot of these practices of opening to the reality of existence. Now, fear comes from thinking of the future and wanting things to be the way we would like them to be. And sometimes when we project into the future we project a limited idea of ourselves, our limited capacities to deal with Dukkha. So accepting and seeing our good qualities, our strength in the present, helps us to understand that we have the Dhamma and a refuge. Strengthening our capacity to feel that refuge within ourselves is very important, so we gain an inner strength. Then our source of happiness is not only coming from others. Developing that sense of refuge, that sense of having a path in life, no matter what arises for us in life.
I remember when my father died, it was this practice of reflection on the universality of death, wanting to be helpful, both to him and to the family, that gave me strength not to think so much about what I have lost, but what I can do for the person who has died, and for the persons who were closest to them. So developing the unselfish emotions and developing especially the compassion/lovingkindness to our loved ones, so that if they do die, we are not just thinking that this is the end of it. We can wish them well wherever they are, continuing on their journey. We can try not to pull them back, thinking they have to be mine, because nothing in this world is mine, or yours. This body, we think it is our own, but all of you have lived long enough to realize that it is not always as we would like it to be. We don't have total control over it and reflecting on the four great elements and reflecting on how it came to be, how it changes and disappears, helps us to understand its true nature. Our loved ones are no different. But fear is an emotion that we try to note when it is present, see how it makes us feel and suffer, have compassion for ourselves and universalize this fear, so that we can get into that compassionate mind, the bigger mind that is able to deal with Dukkha as it arises, as best we can.