[...] I was half-expecting Tobias to reacquire him [...]
I doubt that Dude would let Tobias the hawk get anywhere near him if he could help it.
But, I do hope he lived a full life, and didn't become like Fry's dog there (which, when you think about it, isn't really realistic for a cat to do, waiting around for an owner -- or maybe I've owned really independant cats). But my gut says that he suffered neglect . . .
He was living with Tobias's alcoholic uncle at the time when Tobias trapped himself in morph.
I always thought Tobias didn't really care about Dude, I mean he just left him there, assuming he trapped himself on purpose.
That assumption being a very high probability.
Maybe Dude ran away from home and became roadkill and Tobias ate it.
Tobias couldn't remember how he looked like when he was human weeks after trapping himself in morph, so I doubt he remembered what his cat looked like. Especially when it was crushed by a car and he was literally eating its heart out.