Cell Constance: Could it Stop Cancer?

[plasmodesmata11]

In my textbook, rotifers (and a few other pseudocoelomates) are described as being cell constant. This means each member of a given species has a specific number of cells. They do not divide. Division cannot be induced, and any form of repair or growth is impossible.
It does say that biologists are having difficulty distinguishing the difference between dividing and nondividing cells. So... this post is meant to be a source of brainstorming. We may not know, but there is a nice bunch of knowledge between all the members of this site. So...

Do you think cell constant creatures can develop cancer?
Now I thought about Cdks (cyclin dependent kinases) controlling the cell cycle, but could cancer stop that?
I also thought about the protein p27, which inhibits the cell cycle. Does anyone know anything about it? Could that be what makes nondividing cells the way they are?
Does anyone have any other ideas or possible answers?
Thanks!