How can an insoluble compound be a strong electrolyte Here's a quote from Petrruci General Chemistry (pg. 160):

Silver chloride, $\ce{AgCl}$ is an insoluble ionic compound. When $\ce{AgCl}$ dissolved in water, it is 100% dissociated into $\ce{Ag}^+\text{ and } \ce{Cl}^-$ ions; there are no $\ce{AgCl}$ pairs.

I'm confused:

1) If $\ce{AgCl}$ is insoluble, how is it dissolved in water?

2) If  $\ce{AgCl}$ is a strong electrolyte but insoluble, does it mean a  $\ce{AgCl}$ molecule is ionized, but isn't separated - i.e. the silver and chloride remains close (they're not solvated by water molecules) but each becomes and ion?
I'm confused, can someone explain what's going on?
It sounds contradictory, but soluble and insoluble are relative terms. Silver chloride's $\mathrm{K_{sp}}$ is $1.77\times 10^{-10}$, so one can generally think of it as insoluble, but actually about a milligram will dissolve in a litre of water.

Much like the terms strong acid and weak acid, strong electrolyte and weak electrolyte refer to the dissociation of a substance in a solvent, though they include all electrolytes, not just acids. In the case of silver chloride, though little of it dissolves, what does is present only as $\ce{Ag+}$ and $\ce{Cl-}$, not solvated  $\ce{AgCl}$. In water, all salts are strong electrolytes, but in other solvents, things can be different. For example, while perchloric acid is a strong electrolyte in water, it doesn't dissociate completely in acetic so it's a weak electrolyte.

Source: (1) Electrochemical Dictionary; Bard, A. J.; Inzelt, G.; Scholz, F., Eds.; Springer Berlin Heidelberg: Berlin, Heidelberg, 2008.