The gamemaker "opened the gates" to this question by allowing China to collect income and build units without a capital (or for that matter, and industrial complex). This is kind of an exception to the normal rules of the game. The "fiction" behind this might be that China has a "second" capital at America's San Francisco (Western U.S.). Then the resulting "house rule" would be that China could produce units until the Allies lost its "second" capital at San Francisco. And the Allies could reactivate this (joint) lost production by recapturing either San Francisco or China's capital of Nanking (in the same square as "Shanghai").
These two countries are often played by the same player. (And even if they aren't, during the real World War II, the U.S. took China under its wing,overseeing its command structure and supply sourcing more than the other allies.) So the house rule would allow China to operate under an American "shadow" government. This rule would mirror the Classic version, under which the two Chinese provinces were treated as U.S. "satellites" played by the U.S. player.
Likewise, the UK would have a dual command structure out of (Calcutta) India and (Sydney) Australia. And again, the UK and ANZAC are often played by the same player, in addition to being linked in real life. So if one capital were captured, would it make sense that the country could continue to collect income and build units under the leadership of the other capital; India or Sydney? (If India were captured, production of the combined number of pieces would fall under the limitation of Australia's industrial complexes.) Again, it doesn't seem logical that either India or Australia would stop building units upon losing its capital when there is a "sister" government in the same hemisphere that it can report to. The two UK countries are actually closer to each other than the U.S. and China, so it would make more sense for them to operate jointly than for the U.S. and China.
Japan has no allies, so it would not have a dual capital structure.
This is an "umbrella" rule that 1) "explains" the China exception to the usual rules; 2) provides for the loss of Chinese productive capacity if it loses American aid and moral support and 3) extends the "China rule" to India and Australia. Would such a house rule make sense by making the game 1) more consistent (internally and with previous game versions) 2) more playable 3) more historically accurate?