The wearout point is also determined by the tire section and pressure. On wired-on tires the rim makes up part of the cross section of the tire and must keep the tire from expanding. As you inflate the tire it'll pull the rim a bit wider at the flanges, and as the rim thins it'll reach a point of not being strong enough and fail.
This was a rarity in the days of narrow HP road tires, but mtn tires with the larger x-section and high pressure ratings create much higher rim loads leading to failure. Add to that the higher braking forces applied to the rim, accelerating metal fatigue and you can see the problem.
As another poster mentioned, there are wear indicator grooves cut into some rims, or you'll get some warning of a coming failure by uneven brake modulation as the rim begins to widen unevenly under the pressure load.
Folks riding large section tires at higher pressure need to be most attuned to the problem, which in any case can be helped somewhat by mounting the brake shoes so they press hardest on the box area of the rim rather than the flanges.
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