To the best of my knowledge, the eggs would simply pass through the digestive tract and be eliminated in the feces. As you say, canids are definitive hosts not intermediates.
“Dogs can be considered as rare intermediate host for E.multilocularis.”
This rare case was mentioned in the following paper:
Peregrine, Andrew S., et al. "Alveolar hydatid disease (Echinococcus multilocularis) in the liver of a Canadian dog in British Columbia, a newly endemic region." The Canadian Veterinary Journal 53.8 (2012): 870.
Other paper mentioned unusual presentation of alveolar echinococcosis in dogs which is a case report:
Geigy, Caroline A., et al. "Unusual presentation of alveolar echinococcosis as prostatic and paraprostatic cysts in a dog." BMC veterinary research 9.1 (2013): 1-5.
Besides the two papers mentioned above, Oscos-Snowball and collaborators have recently published an article that again reported the role of the dog as an aberrant intermediate host for E. multilocularis.
Oscos-Snowball A, Tan E, Peregrine AS, Foster R, Bronsoiler J, Gottstein B, Jenkins E, Gesy K, Bienzle D., 2014, What is your diagnosis? Fluid aspirated from an abdominal mass in a dog. Vet Clin Pathol. doi: 10.1111/vcp.12210. [Epub ahead of print]
Yes, it may be posssible, but not common. So, such chances may be more common when cats or even dogs or foxes or other wild canids may get infection with eggs under immunodeficient conditions. I have resubmitted such topics to some journal but not yet been accepted.
Dogs are the final host of Echinococcus granulosus and contain the adult parasite inside her intestines that develope by ingestion hydatid cysts that found in tissues of infected dead and slaughtered animals and birds so dogs cant be infected by eggs of the parasite because the environment of dog intestine isnt suitable to hexacanth embryo to still alive and penetrate intestine wall towards blood stream and formed hydatid cysts later..
It may happen but not common. There are reports showing dogs and foxes harboring both stages, hydatid cysts in the liver, and adults in the intestine. So, the life cycle may be completed by cannibalism of carnivors even though the major cylce is maintained the prey-predator interaction of the different animals of herbivors and/or omnivors and carnivors.
I also would like to ask a question. Could you please explain me how protoscoleces can be alive in gastric acid in canids ? if the protoscoleces are resistant to gastric acid, why don't they infect humans. Because human can be infect with only eggs of Echinococcus.
Some colleagues have pointed to a few reports of dogs infection with Echinococcus multilocalaris cyst.
I think there is difference between alveolar echonococosis and cystic echonococosis. Because the final host of the first parasite is the fox, so the dog may have some susceptibility toward it, while in cystic echonococosis the dog represent the final host here.
Also the eggs of the parasite may be digested in the dog's intestine when ingest it by the food.
Cases are rare in North America. The parasite is transmitted to dogs when they eat organs of other animals that contain hydatid cysts. Once ingested by canines, these cysts develop into adult tapeworms. Infected dogs shed tapeworm eggs in their feces, which contaminate the ground.