The thing with rabbits is that if their fecal poop isn't the normal size, round shape, and friable consistency it's supposed to be, then the rabbit usually has some sort of health issue going on. It can be an underlying health problem, or it can be diet related that has progressed to a potentially dangerous health problem. And like Watermelons mentioned, stress(such as from going to a new home) can also be a contributing factor, causing upset of the rabbits normal digestive microflora and allowing harmful bacteria to flourish. It can start out as a less severe digestive upset where there is some mushy cecals sticking to their bottom, along with producing normal round fecal poop. But in some cases the digestive upset can worsen as the harmful bacteria takes over, and diarrhea then occurs.
If the rabbit has watery or pudding like diarrhea, that is a true emergency, as most often it is due to a potentially fatal gastric illness such as coccidiosis or bacterial enteritis. Diarrhea is especially dangerous when it occurs in young and baby rabbits. Rabbits have a very sensitive digestive process, and any disruption to that can lead to potentially fatal gastric illness.
http://www.bio.miami.edu/hare/poop.html
http://www.medirabbit.com/EN/GI_diseases/drop/Drp_en.htm
http://www.medirabbit.com/EN/GI_diseases/Generalities/Enteritis_en.htm
http://www.medirabbit.com/EN/GI_diseases/Protozoal_diseases/Cocc_en.htm
It sounds like your rabbit probably developed bacterial enteritis, which happens when an overgrowth of harmful bacteria in the digestive tract occurs, usually from either e. coli or clostridium sp. If the diarrhea was brown and not a yellowish color, your rabbit likely had enterotoxaemia from clostridium sp., which is very dangerous and progresses rapidly due to the toxins released. Treatment has to be started immediately to have any chance of recovery.
http://wildpro.twycrosszoo.org/S/00dis/Bacterial/Clostridial_enteritis_rabbits.htm
It's always very important for rabbit owners to be aware of the potential digestive problems that can occur in rabbits including stasis, bloat, cecal dysbiosis, as well as diarrhea, and to closely monitor the rabbits droppings each day, as any change in them can be a signal of a possible health problem developing. I wish all those who sold or rehomed rabbits would share this information with the new owners like yourself, as a majority of fatalities with rabbits in new homes is digestive related. I'm really sorry about your bun and wish the previous owner had passed on this important information to you as it could have possibly prevented the death of your little girl if they had.
