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The most dangerous aspect of the eruption, however, is the ash fallout, both locally and globally.
Breathe this in and it’ll lacerate your lungs and form a glassy cement. It’s also about six times denser than water, which means plenty of architecture would collapse under its weight as it accumulates on rooftops. Poland points out that “even a few tens of centimeters of wet ash could cause weak buildings to buckle.”
Roads and sewer systems would clog and break down, water supplies would be contaminated, and electrical grids would short out. Millions of homes could become uninhabitable.
In this sense, those taking shelter in Montana, Idaho, and Wyoming would be at the highest risk of harm. They would be so for up to a month, which is a fairly solid bet as to how long the eruption would ultimately be.
An area about 80 kilometers (50 miles) around the vent would be covered in 3 meters (about 10 feet) of ash in just a few days. Simulations have also shown that a supereruption could bury Salt Lake City and its surroundings beneath a meter (3.3 feet) of ash.
https://www.iflscience.com/environment/this-is-what-would-happen-to-the-world-if-the-yellowstone-supervolcano-erupted-today/page-3/