You should really learn how to counter somebody snowballing.
For example, if the person who is snowballing is your direct role opponent and they're farming off you in particular, you need to learn how to duel better, manage the minion wave in your favor (minions hurt a surprising amount early game), and how to leverage the lane when you two are even and/or when you're behind.
If the person who is snowballing is your direct role opponent and they're farming off your teammates, you need to know whether your opponent is better off wave clearing (as most mages are) or following/roaming (as many Fighters and Assassins are). It's a lot harder to necessarily stop your laning opponent if they do this, but it's very easy to take something in exchange for them leaving you alone for even a moment.
If the person who is snowballing is not your role opponent and they're farming off you, that's simply a matter of learning how to disengage from enemy ganks or even how to turn ganks all the way around. Learn where's the best place to put your wards and certain tells the opposing laner does that signals that one of their allies is nearby.
If the person who is snowballing is not your role opponent and they're farming off somebody else, you need to gank/countergank them and shut off their snowball before it begins. It's easier to stop a snowball while it's at the top of a hill rather than when it's already huge near the bottom, so you need to learn the signs between whether the other guy just had a bad trade or if he's going to continue losing lane.
And then there's counter building. You absolutely can not not build for the situation. I don't care if you are an ADC, you better build an actual MR item if the enemy Burst Mage is fed. % stats and/or wave clear is your best friend when fighting against fed Tanks. Any items you can buy that either bolsters your burst or your potential to engage on a squishy is godsend against fed carries. It's simply a matter of using the right tools against the right enemy.
