I'm going to answer more generally first: I'm not sure it would really be healthy to. That you are attached to others and cherish your time with them seems healthy to me. If this fear is paralyzing you in some way, I could see reason to be concerned and perhaps urge you to seek out a professional to talk to if at all possible. But if it's just that it occasionally bothers you, that seems pretty human to me.
More specifically: As you do mention some preoccupation with it that you view as abnormal and seem to want to know more about it, I would ask you to consider... is it that you feel you need to understand death so you can cope with it? Is it a knowledge gap? A curiosity thing? If you are someone who wants to be as informed as you possibly can so you can face something, then you may have to either accept it's the one thing about life you will never really know until it happens, or it may help to explore fantasy stories and different religious takes on it to feed your desire to understand it better (if that does apply). Though you can't know, you could get a clearer picture of how human beings tend to view death and what they do about it, dissecting it on a cultural and materialist level, so you can sort of "zoom out" a little.
Another element to consider is, would you consider these thoughts intrusive and obsessive? Because if they are, it may help to practice welcoming them in, rather than trying to push them away (if that is something you think you are doing). Similar to anxiety spirals and being anxious about being anxious, becoming upset about the nature of an intrusive thought can make it worse. (Disclaimer here: I'm not a professional, just going off of what I know from personal research.)