I had 2174 health and 125 armor. Yi 2-shotted me instantaneously, and of course it was entirely physical damage. There is NO opportunity for counterplay against endgame Yi. What can be done? It's pretty obnoxious.
Stop being so close to the front lines if you're a mage, stop being so far away from the designated peeler of your team if you're an ADC.
If Master Yi focuses a bruiser or a tank first, all the carries must focus him.
And stop running around by yourself. Master Yi's strengths rests in 1v1s and pseudo 1v1s, and all his weaknesses rest in team fights. Force him into uncomfortable situations for him.
I usually have around 3000 health and 300-400 armor and I can 1v1 him all day. Sounds like you're trying to fight someone designed to bust squishies as a squishy.
Stun him. Team bursts him down. And if you don't have a stun and you are a squishy, that's your fault for letting him get to you. Well, unless your whole team was just running away and left you to die to him because you can't very well run from a yi endgame unless safety is really close.
Dont be bronze?
After counting LW and Youmuu's, you had like 60 armor. Plus he probably hit you with Bork active, that and hitting Q and double strike will typically shred a squishy.
2 shotted
right
Here are some tips:
Be ranged
Have hard cc (fears might be even better since it makes him run away full speed, ignoring the slow)
Ward his jungle....oh wait, that's Lycan
Don't think you can outrun him
EDIT: DON'T LET IT GO LATE!!!! Seriously. If he gets 
and you let your team let it go late you deserve to lose since you didn't end it before he got a shit ton of damage from devourer
