Probably the parents, potentialy assisted by charitable organizations. In a society that's voluntary enough, the person would likely have the legal option of suicide before taking responsibility for paying for their own rare disease.
If possible, it might be good to show the evidence of the disease prior to birth so that the development can be halted well before birth occurs, mimimizing the likelihood that parents would be faced with an undue natural burden.
A voluntary society probably wouldn't want to force parents to pay for childcare, but it would be hugely unethical to simply let the child suffer and die after birth just to avoid them being an involuntary burden on anyone.
Give the parents the choice as early as possible whether or not they want to assume responsibility for a child with a rare disease. That way if they're required to shoulder the burden, it was voluntary and not just a random natural dice roll that forced them into an unforseen debt.
Frankly, I'm not sure how a voluntary society would handle orphaned, abandoned or abused children. Litigation against the parents might sometimes be an option, but you would need to fund any sort of foster care program. Ideally, that could be done through donations, but if that doesn't work you'd need members of the society to step up and assume moral responsibility for these unfortunate kids. Probably there would be some combination of the above methods.
Another alternative might be child insurance, whereby prospective parents could pay into a system that would help support their child in the event of unforseen circumstances. Parents who don't get this insurance would risk being shunned or facing a lawsuit or something if they child is harmed due to their lack of foresight.
Lots of market-based options, really. If a state wanted to step in, they'd have to find a way to accomplish their goals without taxes or authoritarian force.
