I dont think stygia stuns an entire team. I’ve met her occasionally in pvp and i dont ever see that happening. Unless you are using only one hero in pvp?
From my experience, i can always switch to another hero when she stuns the one im using. Its always a good idea to bring at least 2 or 3 dps heroes to a match just so you can switch to the other when the one you are controlling is down or disabled. Even before stygia was released, i always do that. Are you using only one dps hero in pvp? If so, then its pretty obvious for your opponent to choose which one to stun. You might want to change your strategy and bring at least two dps into a fight. Secondly, stygia is one of the hard heroes to kill… just like Min, etc. Dont waste time trying to kill her first. Kill the easy ones first and save stygia for last. Stygia is hard to kill but not unkillable. Hope my advise helps. I dont always win but i dont always lose either. Best of luck.