For this to work you would need to find an infectious disease that is rapidly fatal and incurable or difficult to treat by modern medicine. I suspect most illnesses which have these characteristics are rare and horrifically painful, e.g. flesh-eating bacteria, biotoxins from contaminated food, or necrotizing parasites.
Other diseases such as AIDS and pneumonia, while easier to catch, would entail expensive medication and a drawn-out, agonizing death.
All the rest probably won't kill you, but they'll require costly treatment and put you in some discomfort.
Though it says something if any of these are preferable to your current life situation.