Yes, I believe I can care for someone without being close to them. Care is not the same thing as closeness. Someone can be close to me yet I might not feel loved, so it's not about distance.
Some people in my life I rarely speak to, we don't call every week or send long messages. But if I hear they are struggling, i would feel it immediately. For me, that is what caring really is: wanting good things for someone whether or not they know it.
The clearest example is a woman I follow on Facebook. I have never met her, and we have never spoken. I only know her through her page and her content, but I love the way she shares her life. Not long ago, she posted about her son's developmental milestones going backwards honestly my heart sank after watching it and I still pray for that little boy even today. She has no idea that a stranger in Port Harcourt thinks of her son. We have no friendship and no closeness, yet the care is real.
I also see this at school. Pupils move on to higher classes or other schools, and I no longer see them every day. But I still wonder how they are doing. Whenever I meet one on the road and they greet me, I always feel proud and will always ask how they're doing. I never stopped caring, we just stopped being in the same room.
Still, I don't think distance should be an excuse. A short message, a prayer, or a simple "I was thinking of you" can mean a lot. Caring in silence is real, but caring out loud is better when you can.
And what about people who are no longer here, or no longer close? I think the care stays. It changes shape. It becomes remembering them, telling their stories, and living the way they would have wanted for us.
So no, you don't have to be near someone to care about them. You just have to keep them in your heart, and reach out when you can.
Care does not need a shared address or a daily conversation, but when we can, we should let people know they matter, because love that is never expressed is easy to doubt.