@Brian Haley
In the majority of states, property value is assessed for property tax purposes every five to seven years. However, some states only assess the value of the home upon the sale or refinancing of the property.
Clayton county confirmed with me that if they did miss an addition to a property, they can't go back and charge you for it but moving forward, once it is re-assessed by an appraiser the new property sqft would be recorded by the county and a new property tax will reflect moving forward.
Clayton County Tax Assessors Info/ Tel#:
https://www.claytoncountyga.gov/government/tax-***...
You can also contact your local government appraiser and or find notice of assessment information:
claytoncountyga.gov > tax accessor (gov tab) > link > assessment > current year > local appraiser / notice of assessment info.
To answer your question no the county cannot go after the buyer for back taxes - they can only re-adjust and apply the appropriate taxes moving forward.