A piece of plastic comes under the category of insulating material and insulators are not able to move/flow electric charge through it. So the piece of plastic generally cannot be charged by the induction method.
A schematic of charging a metallic conductor piece by induction method is represented below.

Here, A is the metal sphere and B is the plastic rod. And E and F denote the locations of negative and positive charges.
Let us consider a neutral metal sphere and a negatively charged plastic rod. From the above figure, if the negatively charged plastic rod comes closure to the neutral sphere, then separation of charge takes place/ occurs.
The positive charges in the sphere get attracted towards the plastic rod and move to one end of the sphere that is closer to the plastic rod.
Thus, the piece of plastic would not be charged by the induction process.