What is this feeling?

There's a peculiar feeling when saying goodbye to someone for the last time. I felt it the last time I saw my grandpa, the last time I saw one of my former colleagues, and with strangers I meet, connect with like they're old friends, and then suddenly depart from. While none of these events can be equated, the same eeriness persists.

What is it? This feeling... with a glint in your eye wishing them good health, the very best, and hoping that someday you might meet again. But somewhere deep inside, knowing it will not happen. At least in this world.