There is a difference between supporting someone and enabling someone. One partner killing themselves for another, at the detriment of their needs and boundaries, mental sanity or even emotional well-being is *not* support. This is not a healthy relationship. What Partner A is doing is only teaching Partner B that they can sit back and do nothing. Sorry but the responsibility here goes both ways.
Instead of killing Partner B or yelling at them (after all, Partner A taught Partner B that this behaviour was acceptable anyway): the relationship dynamics need to change. Partner B who is luxuriating in their partner doing everything for them needs to get their butt in gear. And Partner A needs to stop doing every single thing for Partner B.
That is, IF Partner A wants to stay in the relationship.