The risk of not upgrading once extended support ends is that systems running Windows 7 will become vulnerable to un-patched security risks within the OS and the applications it runs.
The main concern would be that once the security updates stop, the OS becomes vulnerable and an easier target for hackers. The fact remains that unpatched systems are vulnerable not only to known attacks, but also to as-yet-unknown attacks that are sure to come. Having an up-to-date antivirus engine installed would be mandatory
Applications might also end their support/functionality on the OS due to the outdated nature and security risks. This will cause compatibility issues and will increase the time needed to keep the applications running optimally, reducing productivity.
The overall impact would be that the systems would incur a much higher running cost, due to the previously mentioned points.