unless you live in some 4th world african country where people are starving you already get plenty of protein
i can tell you what happens when you get TOO MUCH protein like we do in north america.. we get fatter and fatter. go watch what people look like when they leave a steakhouse, they aren't ripped 5%.. they are fat and obese
Your body would start to catabolize muscle tissue for amino acids but like the posters above commented - not getting enough protein really isn't something you have to worry about in North America. Most of us actually consume too much protein