Zs capuring a capital
Zs capture a territory during Phase 3 of a turn. So if enough Zs end up in an otherwise ‘empty’ capital the Zs will take over this capital.
(See: Phase 3 / page 14 / right column)
As far as I know this can happen:
When an enemy attacks your capital and only Zs are left after combat. Then during Phase 3 of the next turn the Zs will capture the capital and take the money.
When you yourself (or an ally) attack the Zs in your capital (which is still controlled by you at that point) and after combat only Zs are left (so they capture capital in next turn and get the money).
When during Phase 2 (Zs Attack) all of your units are destroyed by Zs.
(This is pretty unlikely as the Zs in this phase only hit at 1/6)
When enough Zs are moved into your capital by cards or technologies.
Anyway, the actual capture happens in Phase 3. But at page 23 (left column) under 'Step 9: Conclude Combat and Capture territory it also mentions: “If the Capital was captured by Zs…”.
But this does not happen in that very moment of the game.
PS: I really like the concept that a capital has a certain resistance/buffer against being taken over by Zs…