This describes a friend of mine, and that makes me sad. Our conversations are either about cats, about her, or we don't talk for days and days. It used to describe another friend, but after a falling out and not talking for months, we've reconnected in a way that works. There are no more expectations, by either of us, to always be there. But we still have a lot of compatibilities, and occasional chats are enjoyable when neither of us expect anything from the other besides someone who understands. It's understanding without taking on the problem as a caseload. I still don't know what to do about the first friend, though.
Regarding the first friend: If there is a long-standing loyalty or debt of friendship or important past shared experience, you might want to continue the friendship in some form. Decide how much of your time you can afford. Protect yourself by combining time with that friend with another activity that you have to do. The person might move from being a caseload to being something else.
We definitely have all those reasons to remain friends, and she wasn't always a caseload. Currently my approach to stay sane is when she stops replying to messages, I stop caring. It's effective in making me not feel cast aside, but the consequence is growing apathy toward her.