Carnivorous plants use a variety of enzymes, including proteases which digest proteins to provide the plant with nitrogen. You might think that the hard exoskeleton would not be digested but pitcher plants (at least some types) produce chitinases which dissolve chitin (i.e. the exoskeleton), so there should be nothing left of the prey. The enzymes are secreted by tiny glands inside the pitcher.
The enzymes that have been detected in carnivorous plants include amylase, chitinase, esterase, lipase, peroxidase, phosphatase, protease, and ribonuclease.
From the Sarracenia faq.
Aside from the enzymes secreted by the plant, there are micro-organisms present in the pitcher which will dissolve organic matter.
In my experience of growing Nepenthes and Sarracenia it seems to take a long time for the prey to dissolve and there is always some material left. Which type of pitcher plant are you growing?
There's a good description of CP digestion from the ICPS.
A more technical explanation about chitinase.
I can't find any specific detail on how the plant absorbs the nutrients, though even non-carnivorous plants can absorb nutrients through the leaf surface.