The health screening is extremely rigorous. They are isolated for a while before launch. They are also trained in basic medical stuff, and usually they are not alone, so another astronaut, either American or another country, will be there. Something serious could definitely happen, though.
These days, it isn’t too hard to get another rocket up there on short notice. So unless it is rapid and dire, the odds of a death are low, but definitely a non-zero chance.
Side note. You should read [an astronaut’s guide to life on earth](https://www.walmart.com/ip/An-Astronaut-s-Guide-Life-Earth-What-Going-Space-Taught-Me-Ingenuity-Determination-Being-Prepared-Anything-9780316253031-Used-Pre-owned/1354684905?wmlspartner=wlpa&selectedSellerId=2157&adid=22222222228000000000&wl0=&wl1=g&wl2=m&wl3=42423897272&wl4=pla-51320962143&wl5=9009739&wl6=&wl7=&wl8=&wl9=pla&wl10=408257971&wl11=online&wl12=1354684905_2157&veh=sem&gclid=CjwKCAjw-7OlBhB8EiwAnoOEk2dk4nOU7_FluAljJZpTwXXsR6dQyQcseMD5dvEW_Dov26m6ajnEXBoC3GsQAvD_BwE)
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