Yanggen chumocho gåmson i ga'lågo, siempre nina' dåkngas.
(If a dog eats octopus, it will lose its hair.)
Ilek-ña i amko', "Ti debe de u chochocho sa' måppla' siempre i pilu-ña." "It shouldn't eat it because its hair will fall out"
I heard this when I was a kid.
Not that I have ever seen it. Fifty years and I have not once seen anyone offer octopus to a dog.
So I asked the elder, "Lao håftaimano i ga'lågo para u fañodda' gåmson para na'-ña?" "How would a dog find an octopus for food?"
"Yanggen mañochocho gåmson i familia ya guaha sopbla, siña ha' nina' chocho gue' nu i gamson." "If the family is eating octopus and there are leftovers, the family might make the dog eat the octopus."
Neither is there, as far as I can find out, any scientific basis for the folk belief.
The only caveat I read about is to avoid the toxic blue-ringed octopus. Its venom is powerful enough to kill humans.
"Don't eat me! I'm poisonous!"
But I'd never myself offer a dog even a regular octopus. Just in case.
This seems to be more than just a Chamorro concern, as the link below will show. Others have also asked the question if eating octopus will make a dog lose its hair.