I would agree with Jan that it's an issue of motivation rather than 'caring'. It has to matter what happens in the story, or else why read on? It could be that your characters are emotionally involved with each other and the reader identifies with (at least) one character, and so they care what happens - but to me that sounds more like literature than mystery. Or it could be that something in the storyline matters to a particular character - a character the reader identifies with - like maybe it's the last chance for this detective or PI? There has to be a character that the reader identifies with, is rooting for, and there has to be something happening in the story that really matters for that character.
Maybe the difficulty you're encountering is not about conveying caring, it might be something as straightforward as point of view. I don't know if other writers would agree with me here? Certainly I find that unless you manage that trick of getting the point of view really close to your main characters, then the whole story can seem a bit 'so what?' Maybe you really need to zero in on one character, think hard about what matters to that character, and make that one person your main POV character, see everything through their eyes. What matters to them will then matter to your reader.
I hope you won't be discouraged. I think imagination is everything. I've never been through cancer treatment, but I've been through childbirth a couple of times and it was dreadful (and nearly deadly on one occasion), but really nothing unimaginable for someone with imagination. Before I was a parent, I used to be nonplussed by friends who were parents who used to suggest the whole experience was utterly beyond someone who hadn't done it. Well, they were lying or lacking in imagination. Imagination requires depth of experience, I think, it doesn't demand that you have been through a specific experience yourself, but it requires you to have been pushed into particular emotional zones (like loss, love, helplessness, hate, self-loathing, whatever). So long as you have enough depth of experience in those zones, you can generalise them from one experience to another.
Don't be put off. It's probably a matter of craft, in terms of writing technique, and instead you're thinking it's something to do with you. I would bet it's not.
Best of luck
Deborah.