You have to try and collaborate, try and help, but at the same time you have to meet your responsibilities.

Management has to see this, perhaps by dividing responsibilities and letting management see that the other person can't handle the load. It is ultimately the responsibility of the manager to find a place for someone or get rid of them. There isn't a great shame in asking someone to move on if they aren't a good fit. Doesn't mean they can't work in the field, just that this might not be the place for them.