Yes, but it can give you a serious illness, so don't try it.
Actually, vegan animals often do eat their own feces. The reason is that their digestive tracts are too short to properly digest the plant matter. So they eat it again. Cows are vegans, but they have a different mechanism for dealing with this. They have 4 stomachs and are able to regurgitate at will.
Carnivores and omnivores have no real need to eat their own feces, but some do for other reasons. Certain mammals have a cleaning instinct. Puppies tend to need help learning how to defecate, so their mothers lick back there to help stimulate the process. But sometimes they acquire a taste for fecal matter.
According to the flag report, you can live without a small intestine and on an IV drip. However, it is arguable that you cannot live a normal life without a small intestine, as otherwise you are constantly attached to an IV.
A guess: because it is water soluble.
because the sky is blue and pink