What are my options if I get caught out by 
I legitimately have a 100% death rate when playing those champs when I come across them.
I can't get away and I can't get close to them.
Is this a situation where I simply shouldn't go out alone if my team loses vision of them?
U have problem sticking with shyvanna? Why? Blade of the ruined king+ ultimate should be enough.
build defenses against them, swifties preferably because they both have slows, but yea you're not supposed to be able to just walk to them and kill them, thats the point of kiting and thats a juggernauts weakness. you gotta either flash on em or find the right oportunity, ashe is less mobile so getting swifties would be easy to counter her, she's pretty weak rn so i wouldn't even focus her over a midlaner unless she was fed
Having your support pick up 
or 
will do the trick. 
help. If you're playing someone tanky you could probably take yourself since you can't depend on other people in SoloQ. Having a 
as your AD carry if you're playing with a buddy will work too. But yeah not going out without vision is a good idea. Juggernauts thrive in chaotic teamfights where there's too much going on and the CC is just flying around to other targets. Just don't bother trying to kill them yourself, you're better off playing a "goalkeeper" style and defending your AD carry and letting them take down the frontline. Juggernauts are just kited too easily which is why you don't see any played on a professional level (except reworked at worlds on the juggernaut patch) where even a 
will kite them for weeks. The only reason he was even played then was because he was BROKEN and they built entire comps around him.
Swifties, then mindlessly run at Ashe and she dies. In the case of Kalista, just walk away and not kill her? lol
I honestly don't bother killing Kalista as an immobile champion unless she face checks me or my team ccs her.
