Poor Dude :c
Imagining that Tobias' uncle didn't even notice Tobias was gone, he probably didn't even notice he had the cat either.
Knowing cats (having three myself) I would imagine Dude would just wait until Tobias' uncle opened the door to go out/come in and would make a run for it, then probably never come back, and even he did return Tobias' uncle probably wouldn't let him in.
So, I presuming Dude either became feral or found a new home.
Or he died. I mean, this is Animorphs. A pet's death, especially a pet like Dude who was only brought up once in the whole series, and the first book at that, wouldn't mean a lot to them.
Good point
I think maybe K.A. might have forgotten about him xD I know that happens to me sometimes when I'm writing, I'll bring in a character and then be like, "Aw, forgot him again" or this author called Erin Hunter who repeatedly kills her characters off only to reincarnate them later xD That and she has gender bender problems- guys turn into girls and vice versa... xD