I'll try to explain it with an example:
My country (lets call it Zimm) has 100 IC another country, lets call it Eutopia, also has 100 IC. Both countrys have one single province.
Now, I declare war to Utopia, this increases my dissent 20% and thus, lowers my IC in the same proportion to 80 IC.
My consumer goods demand (that means the amount needed to avoid my dissent for either raising or going down) is grately reduced since I issue the war declaration as we are now under a war economy.
I march over Utopia taking over their only province that same day, this effectively destroys their IC but after 100 days Utopia recovers all their IC (1 day for each IC), my economy is now:
+100 IC (original size)
- 20 IC (caused by dissent)
+ 25 IC (Utopian economy).
Total IC 105 IC.
Now I move the slider of consumer goods to the far right corner and wait for the dissent to lower (this is the only way to reduce dissent, the further right the slider is, the faster my dissent will go down). After a couple days my economy is now 125 IC total.
Now I go to the diplomatic screen and efectively annex Utopia. Zimm's total IC is now 133.
Finally, as jmpt very well said, if you run out of resources, your economy efectively collapses. This may be caused by a bug known as "negative values" which reduces all your resources stockpiles to zero (or even negative!) values after you conquer another nation's capital.
If this happens I'd recommend "cheating" for the resources as that reduction was causes for a bug, this shouldn't be cosnidered a cheat.
Hope this helps.
Regards,
El Basto.