Unus is usually used when you insist that there is only one. So here it would mean "the only one that has been loved".
Idem used like this looks a little weird to me - we don't need a "double subject" - amatus and idem. If idem is the subject of non moritur, what is the verb of amatus? The only way it can be interpreted is that there's an implied est. So your sentence means "only one has been loved, that same one does not die". .
EDIT: Or as amatus can also be a noun, "beloved": there is one beloved, that same one does not die".