Difference between Lineage OS and Cyanogenmod : how does it affect current users? Cyanogen said it plans to cease developing its open-source version of Android and will shutter its services by the end of the month. The company's blog mentions,


  As part of the ongoing consolidation of Cyanogen, all services and Cyanogen-supported nightly builds will be discontinued no later than [December 31].



Do users get new update as OTA while using CyanogenMod, or do they have to completely erase and flash a new ROM? (That requires flashing new firmware, ROM, recovery etc.)
What will happen, if users are continue using CyanogenMod after December 31, 2016? 
What about bugs, security, stability?
Here are some answer, but as I'm not Cyanogen representative, they only engage me.


Users will not receive OTA updates as soon as they stop maintaining their software stack. You keep on using your last Cyanogen ROM and hence receiving no more security updates, or you can change the ROM you install. For changing, you could use an entirely new one and try to wait some guys start a fork of the project (this will, for sure, occur: perhaps you'll be one of them). With a fork it is possible they will choose to support upgrade from the last Cyanogen.
Nothing, you just will not receive updates and you will risk more and more because of missing security updates.
As you will not be able to update, your phone will keep the same software stack as it is. Bugs, security and stability will stay as it is in your last Cyanogen. For bugs &amp; stability, you don't care but for security it is a pain (as security will go down as time goes on).