You grieve for all losses, not just "people" you lose. Anything important to you that is lost hurts and you grieve. You can grieve for a pet, a lost job, even a lost personal item/favorite piece of clothing that is worn out and has to given or thrown away.

So yes, like people caring for parents or spouses with Alzheimers who are no longer "there" or children who have grown and are off to college (empty nest syndrome) all of our lives have lots of various losses that are grieved even when things look like they're really going well (houses and friends we have to leave when we move for a job). If a friend or loved one appears emotionally lifeless and we feel powerless or hopeless to help or get our loved one "back" then yes, I'd think one could grieve for that but I'd worry about the thin line surrounding giving up or feeling hopeless.

As long as there is life one should keep struggling to be and help others to be the best they can, encourage and hope for others who are tired or have no hope of their own. I remember my therapist being worth her salary for merely being my "hope" at times, bucking me up until I could take over at time. It's hard to know why someone else "checks out" but sometimes it's good for us, as well as them, to keep on keeping on trying to help them. That does have to be measured against our "strength" though (not necessarily our wishes/desires), our own health comes before anyone elses as we can't continue to live our own lives, our "purpose" in life, if we wear ourselves out helping others or ourselves when we should be looking after ourselves instead, recouping our strength.