If you Annex a territory that's linked to a city and that city gets occupied by someone else, the annex just stops and all the money you spend on it is gone. 

How did you even annex the territory? I tried to use this ability many times, but never succeeded, no matter what my setup was.

gbowee wrote:

How did you even annex the territory? I tried to use this ability many times, but never succeeded, no matter what my setup was.

See this post.

https://www.games2gether.com/amplitude-studios/humankind/forums/171-bug-reports/threads/39652-ui-bug-annex-territory-costs-800-chickens?page=1#post-316570

gbowee wrote:

How did you even annex the territory? I tried to use this ability many times, but never succeeded, no matter what my setup was.

Be expansionist, have open border with the guy you want to annex from. Don't be at war with him either.