MTG: Can a creatures Toughness go below 0?

Example. Rhox War Monk 3/4 Lifelink attacks Kitchen Finks 3/2. Now a buddy is sayin that you only gain 2 because Kitchen Finks only has 2 toughness. I'm saying that it deals 3 damage making kitchen finks a 3/-1 and you gain 3 life. Seen a couple of rulings saying that once a creatures toughness reaches 0 OR LESS that it's put into the graveyard so I think I'm right. Appreciate the help