For starters, this answer for How are the total possible trophies awarded determined? is closely related. But it's missing a detail that I think you're actually trying to ask.
You are awarded a portion of the available trophies based on the number of stars you earn during the battle. You earn 1 star for destroying the Town Hall of the base, 1 star for destroying 50% of the base, and 1 more star for destroying 100% of the base.
So, let's say you've launched a raiding attack on a resource-rich base that is worth 30 total trophies. This means you'll get 10 trophies for each star you earn. You've snagged all of the resources you are interested in and you're open to ending the attack early. You've dealt 46% base damage so far. If you stay in the attack a bit longer and do only 3% extra damage, then you'll not earn any additional stars at only 49%, so you won't earn any extra trophies. If you do 4% extra damage instead, then you'll reach 50% damage done, which is an extra star and you'll earn 10 trophies.
Situationally, this probably depends if you've already destroyed the Town Hall or not. If you've destroyed the Town Hall already, then you've already earned 1 star and completed a successful attack. So, you'll earn the successful attack resource bonus for the league you're in and the extra trophies you'd earn aren't really a big deal. If I've yet to earn any stars, I'll usually let the attack ride on the off-chance that I can reach 50% and earn the bonus resources.
But, is there a reason why some would want to actively avoid earning more trophies?
Yes there is. Many long-time players target certain leagues to be in for either raiding or resource defending purposes. Certain Town Hall levels will prefer to be placed in certain leagues in order to see more desirable bases to attack, or be in a pool of players that could do little damage in an attack. If you're earning extra trophies that you don't really want, then you'd have to launch attacks just to purposely lose and shed trophies to keep your spot in your preferred league. Or, you could just avoid earning trophies you don't really need.