Some go bad but normally takes a long time. The insulation cracks and wire braid is partially cut. Multiple layers of electrical tape can keep the saw limping on. On my 40yo 011AVT that the plug wire insulation cracked with central wire protruding and some braids cut. Dig the old wire out. Clean up the well. There is a threaded central cone that the new wire will twist onto. Epoxy new wire in. Many wires are 5mm, which is harder to find. I have used 7mm car wire and shaved 1mm off the insulation in last 1/2" to fit into the well. Part of the equation: Is a new AM coil available at low cost for that particular saw? May be an easier route.
Most cannot be replaced without replacing the coil. Some engines (like motorcycles/ATVs) use actual stranded wire, they rarely fail.
They do, but it's not as prevalent as automotive engines for several reasons. The number 1 cause of death for small engine wiring is rodent damage, not heat or old age. The wire is easily replaced only on a minority of modern small engines. Usually it is permanently bonded to the ignition module and the whole ignition system is replaced if it gives trouble. On an automotive engine, the spark plugs and the wires are commonly routed in areas subject to lots of heat from exhaust manifolds. Most small engines have the ignition system including the wire located directly in the stream of cooling air before it passes over the cylinder cooling fins. Failed ignition wires on automotive engines is fast becoming a thing of the past as most built in the last 15 years or so have migrated to systems that eliminate the wires.