Human stool, on average is about 25% solids and 75% water. Up to 54% of the dried solids consist of bacterial biomass, of which protein comprises up to 50% (1). This is pretty consistent with other research that stool contains up to 25% protein (dry weight) (2), although there is still debate over how much of that is attributable to undigested protein and how much is bacterial biomass.
Basically all dietary protein is absorbed in the duodenum and proximal jejunum (3), so, pretty much just the first half of the small intestine. And, since the food you eat only spends a finite amount of time in this region of the gut, protein uptake is likely limited by transporter density and also by the kinetics of gastric and pancreatic enzymes that break down large dietary proteins into small, absorbable peptides and amino acids.
Lastly, when your body does uptake more protein than it needs (or can utilize) at a given time, it doesn't just backlog (there is no storage form of protein in humans). Instead, it's catabolized and used to generate glucose or ketone bodies, which can eventually be stored as glycogen or fat. These processed also generate a significant amount of ammonium waste, which is converted to urea in the liver and excreted in the urine, putting extra strain on the kidneys.
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APUS: An Introduction to Nutrition 1st Edition (Byerley); Chapter 5.4: Protein Digestion, Absorption and Metabolism. https://med.libretexts.org/Courses/American_Public_University/APUS%3A_An_Introduction_to_Nutrition_(Byerley)