A document referred to someone applying for an Australian carer visa in order to care for a relative who was referred to by name and as the sponsor, the Australian relative requiring care and
Caree, as the reciprocal of carer, makes sense and uses an established pattern of English words, and it it is difficult to think of any other suitable word, but it looks and sounds very strange, and is very, very rare. Google first asked me if I meant carer, then career, and Pages for Mac changed it to career (even though that doesn’t make sense in any likely context).
One of the few official sources in which I found it used is the Australian government’s Social Security Guide (which was not the provision in question in the document I was editing). It simply says that a caree is “a person receiving a substantial level of care” and a carer or care provider is “a person who is providing a substantial level of care to a caree”.
Not surprisingly, Google Ngrams shows that the usage of caree is minimal. Surprisingly, it shows that carer has been widely used only since the late 1970s. I don’t know what people providing care were called before that.
I can’t recommend or not recommend caree. I doubt if any writers of government guides are going to check my blog before they use it.