Most amateur builders know it's best practice to add some sort of sealant to the cut ends of a section of firesleeve before installation. This not only controls stray glass fibers, but also prevents flammable liquids (fuel or oil) from being absorbed into the glass fiber matting.
There is, of course, a product sold for this specific application, but everyone does a double-take when they see the list price of a quart of this stuff. Though it took some searching, I found a useful thread on VansAirforce that describes the simple dilution of some 3M fire barrier caulk with xylene. 2 parts xylene to one part caulking, mixed 5 min with a stick, gets you what I consider the 'right' consistency. Dip each end of the firesleeve and let it cure. The curing of this diluted 'dip' takes days, not hours, so find something else to work on while you wait.