Will my CF 2016 Enterprise Edition will turn to developer edition after license expiry?

Cf licenses are typically perpetual ones, so there's no "expiration" to worry about.

That said, Adobe has in recent years offered also optional subscription licensing (not sold on the cf site) as well as the option of using an Amazon AMI (sold on the aws site). Unless you're using one of those, again there's no "expiration" for you to worry about that I know of. 

On the other hand, if you instead install a cf TRIAL then that WILL expire in 30 days, and unless you provide a license key sooner THAT will then revert to the developer edition.

One last thing: Cf2016 is no longer supported/updated since its 5-yr anniversary in Mar 2021. Adobe also no longer sells any version older than cf2021.

If somehow you feel you still have your original worry, and/or you don't hear from anyone else here, you can reach out to cfinstal@adobe.com and they can get you the answer for your specifIc license.