What happen if the fur was close to the paper after the rod and fur were rub together?

The paper will get attracted by the fur. This is because of static electricity, which means electricity that is not moving.

Let us take a brief look on the structure of an atom for better understanding of electrostatic charges.

An atom has protons which are in the center, positively charged, and electrons around the center, negatively charged.

When you rub the rod with the fur the negatively charged electrons stripped away from the fur and transferred to the rod. Because the electrons are in the rod are more tightly bound than the fur. With this, the rod gets more negative than positive charge, whereas the fur gets more positive than negative charge.

Because this extra positive charges, the fur attracts the neutral charged paper.   

One more example for the static electricity is "a pen rubbed with piece of cloth will attract small pieces of paper"