Someone in China may earn a fraction of what the equivalent person does in the US, but may have a similar salary in purchasing power adjusted terms.
Considering only goods that are neither imported nor exported, this could in principle happen, although I doubt it ever gets as far as equality. But considering goods that are either imported or exported, the worker with the lower wage will always have a much lower purchasing power. This is because the market for these goods is international so the tendency is for these to cost the same in international terms in both locations, so the guy with $100/day can buy more of them than the guy with $10/day.
Considering only goods that are neither imported nor exported, this could in principle happen, although I doubt it ever gets as far as equality. But considering goods that are either imported or exported, the worker with the lower wage will always have a much lower purchasing power. This is because the market for these goods is international so the tendency is for these to cost the same in international terms in both locations, so the guy with $100/day can buy more of them than the guy with $10/day.