If you worked at the big corporation where I worked, and they became aware of your side work, they would have asked you to either give it to them if it was of significant interest or leave the company. A former coworker of mine found himself in this situation and left the company.

I found myself in this situation too, but after an investigation the company was not significantly interested in my work enough to pursue it further.

Edit: I should add that plenty of groups within our company, while officially bound to the same agreement, were unofficially free to do similar work without consequence. Our group suffered from a leader who wanted to do things "by the book".