Inductor almost never fails. It's just wires around metal rod (or air core, no metal anything within wire coils) and since it uses no chemical (like caps), and not sensitive to static electricity (like ICs) it almost never fails. Overload and excess heat can kill it but if you got overload or extreme heat, the whole GT would probably be melted into black puddle.
Glue are often used because the coils are known to whistle or squeak, and to protect air core coil from being dinged or bumped which could change the induction quality.