Beings like Trinimac and his relatives weren't exactly mortals, nor exactly Divines in the strictest sense. They were the Ehlnofey. They were powerful ancestor spirits, who were in my opinion a sort of in between stage connecting the Divine with the mortal. I believe Umaril's father was one, as were beings like Morihaus the Bull and other figures of the past. These were the ancestor spirits who called the Dwemer "dwarves", because they stood on average at least twice as tall as modern races on Tamriel, and so their little Dwemer friends would appear as dwarves next to their stature.
Owing to his semi Divine nature, Trinimac's body and spirit were corrupted by Padomaic energies and he was reborn in a hideous form. Would this happen to a mortal? Well, we do know that spirits like Clavicus Vile and Molag Bal can claim the souls or mortals. What they actually choose to do with these souls is up for debate. It seems more logical they would torment them for amusemant rather than transform them into lesser Daedra, but it's possible since the mortal races are supposedly descended from the Ehlnofey, and in turn the Aedra.
Interesting take on it Hairdo, this would also explain how Umaril, having a divine father and mortal mother, was able to become partially, but not fully, Daedric. And why Malacath is weaker than the other Daedric Princes and not considered a "true" Prince by the others. And how Jyggalag changed so drastically when he became Sheogorath, while the CoC didn't change nearly as much upon becoming Sheogorath.
From what I understand, the Daedra and Aedra are labels to classify the various et'Ada; it appears that it is possible to change them so that they would fall under a different label.