This is according to this support page where Google states that some Nest devices will be eligible for a free replacement in the event they are stolen. According to Google, this includes the recently announced battery-powered Nest Cam and Nest Doorbell, along with the wired version of the Nest Doorbell.
In the event that those devices are stolen, Google says that you should file a police report and get a copy of that report, which you will then need to provide Google with in order to prove that your device was stolen and to get a replacement. Google is also saying that you should contact them within 30 days of it being stolen and they will then guide users through the replacement process.
The company also cautions against users removing their camera or doorbell from their account in the app as they will need this information to process the replacement. Unfortunately those with older Nest devices won’t qualify for this, but if you are planning on buying the newer models, then you will be covered.