Usual failures are electrolytics, going high ESR - is the PSU still working OK, apart from the noise?.
The only 'fault' that could cause the inductor to whistle is loose windings, and that doesn't appear to have the windings fixed in any way - and it wouldn't affect operation.
I've repaired huge numbers of SMPSU's (thousands of them over a long period), and have never had such an inductor fail - there's not really anything to go wrong with them, and as it's a thick piece of wire it's unlikely to break.
As you can clearly see from the PCB picture, it's simply a two wire inductor, the extra pins are for mechanical stability.