When full, the core acts like an incinerator. This is so that predicting the rate of gaining resources is more accurate.
Ick. I want my side storage to fill up once the core is full and to stop using resources making the higher tier items. Oddly enough it looks like it actually sends the materials into your global supply, I noticed.
Once I hit 4000 I noticed the global supply continued to rise. There should be options to control what the core does when it's full.