About the accumulated weight of many tons of fluff on my roof? Not a whole lot I could do about that.
The home has attic loft rooms, with about 45deg peaked gabled tops. Much of the ash would stay stuck fast to the textured tarpaper shingles up there but my state is also well known for having high incident winds, gusting up to 40 to 50mph, regularly. Unless it rains, and puts concrete on the roof, much of the ashfall will blow off the roof.
Sadly, that much particulate matter in the atmosphere would likely trigger rain, as it would essentially be cloud seeding.
I would simply have to hope for the best as it rained mixed concrete everywhere for several days. Before the roof caved in, there would likely be several noteworthy warning signs I could observe, such as groaning sounds, cracked door frames, and stress fractures in the afore mentioned attic rooms. If I suspected imminent roof collapse, I would find a TINY downstairs closet space, and grab the hatchet and limb saw I keep in my utility room, then set up shop in the smaller, more structurally sound room. Going outside would be suicidal, until all risk of asshfall had ceased.
Quite literally, the rock and the hard place.
I would do the best I could, given the situation.
For an example of what Yellowstone exploding would do, go to the fossil record of
its bigger sister in indonesia. When that one went off, the human race nearly went extinct globally.
That should help answer your question.
However, regardless, it is simply outside human capability to avert. Worrying about it is a pointless exercise. I merely responded to the "What would you do?" question.