For example, unburden Hawlucha dropping below 50% HP and consuming a Sitrus berry.
Hawlucha has 328 Speed - Unburden should boost that to 656 when consuming the berry, allowing Hawlucha to outspeed any unboosted pokemon. However, Reukra's shadow Mewtwo still outspeeds Hawlucha after eating the berry. I'd bet this would still happen when consuming any other held item (eg focus sash), or by using Fling, though I haven't tested those cases.
Playing on hard mode FWIW.