None that I am aware of... in fact they could cause an asthma attack!

It depends on what is triggering the attacks. If it is indoor chemical air pollution, such as formaldehyde, some plants, such as Spider Plant (Chlorophytum comosum), might prove useful. If airborne dust or spores, most plants, either the leaves or the soil, will make it worse.

Those few that are suggested seem to work - if they do- by improving air quality. You could do this more efficiently with an ioniser. if you stand a little ioniser on a sheet of white paper you'll be amazed at the amount of dust and dirt that lands on it!
Peace lilly has been suggested as helpful and might be worth a try but you'd probably need lots of them to make any difference...

Agree with Tugbrethil - depends what the asthma sufferer is sensitive to. Often its dust mite or their droppings, or general dust, sometimes pollens, sometimes moulds. Both the latter are more likely to be in the air if you have houseplants. Having raised two asthmatic kids, and now suffering myself, dust seemed to be the biggest daily factor, so your best friend is a good vacuum cleaner with a HEPA filter and a damp cloth for dusting - daily, and vacuuming mattresses and curtains weekly. Nowadays, of course, if you live in a city in the UK, high air pollution contributes and exacerbates the problem, particularly if the weather is very still and hot.

Artificial houseplants made of silk, fabric or plastic are the only ones that are safe.

And also need frequent dusting--with something that traps the dust--to keep the allergens down. Hmmm...not so different from real plants, that way, though! :)

Well, might as well have not a stick of furniture in the home to collect dust. I prefer to stay on deck and not go overboard.

I have a great tip for cleaning artificials. Pop them in a bin liner with plenty of table salt and give it a good hard shake. The salt attracts and knocks off the dirt. It works a treat!