Is she out there?
yeah, yye poly. You don’t need some mythical string that does tricks for you, you just need to practice.
No poly doesnt handle tension well ^^^^^^^^
Yes it does.
Poly can be very soft, and can handle tension.
That said, YYE Poly isn’t particularly soft.
Nor does it whip that well. At least not by comparison to many other strings.
The “thin side” of things limits your choices. You would probably need to go with something based on trilobal thread, which will take away from the “softness” factor. It’s a major balancing game, and I don’t think you’re likely to hit all those bases. Might be time to pick your two most important ones and go from there. 
Quick 13’s T13x is on the thinner side and whips amazingly. It’s not “rough”, but it’s also not particularly soft… it’s just got that plasticky trilobal feel to it, so it depends on your definitions of “soft/rough”. Tension… well, it’s not anything special. Not terrible or anything, but there are better strings for managing tension.
So there’s an example for you. Thin yet whips well. Had to sacrifice some softness and tension management to get’r done.
Lol I mean it’s not like 90+% of yoyoers use it or anything and it works perfectly fine, right?
YYSL AMMO and BYYS 3lan Muse meets all your requirments except being thin.
Kitty String Thick, nuff’ said.
Well YYSL type X is thin.
It’s not as soft though 
You’re going to have to pick from thin string or soft string because you can’t really have both…
Type X is pretty soft. And pretty thin. But it doesn’t whip very fast. I throw out my shoulder when I try to do a Brent Stole with it.
I’d say BigYoyo 3lanMuse is the way to go. It lasts a good while, too. Andy569 is right, you’ll really can’t get thin and soft and whippy all in one.
This.
Thin, whippy, or soft. Pick two. You can’t have all three.
Thin (light) strings don’t whip as well as thick (heavy) strings.
Strings made of dense material aren’t soft.
So you really can’t have all three.
BigYoyo String—Candy String.
It fits most of the specs you’re looking for.
Pm BigYoyo or myself if you want to try them.
This. Stuff is crazy good.