What do you call a possum's nest?

Possums do not have nests. They shelter in hollows within trees, and in other enclosed spaces such as roof cavities and chimneys.

It should be noted that possums are not the same as the opossums of North America, even though both are marsupials. Some sources may report that an opossum's nest is called a "drey". This term applies to squirrels, which are members of the rodent family, not opossums (or even possums).