The first thing I noticed arriving at the inspection was the darkening around the vent cap for the pellet stove.  A pellet stove can be side-wall vented, if it’s done according to the manufactures instructions.        

But (yikes) this one had single wall flex pipe inside the wooden chase

with no clearance to combustibles.

Something like the above is what you should see instead of the flex pipe.  Double wall, type L stove pipe with the proper clearances from combustibles.

But let me back up a little:  what is a pellet stove?  they are like regular wood stoves but they burn pellet, or corn, or sometimes wood chips.  They have their own sealed venting fan system so they don’t need the draft of a chimney.  Modern ones operate on a thermostat and light and go out as necessary.

At this inspection, though, the pellet stove did not have it’s dedicated outside air supply that brings combustion air from the outside.