In most cases, yes. A car will be accompanied by the original papers if they were mentioned in the description. Occasionally, cars will be sold without papers.
After the seller has de-registered the car, they will receive new papers indicating that the vehicle is no longer in the national registry of that country. You'll need these papers to register the car in another country. In some countries, the seller can only complete this procedure once the car has been exported.
When a vehicle doesn’t have its papers, it is possible to request a new document and later a new registration and number plates through clubs and associations. These local organisations will be able to guide you through the process.
As there is no all-encompassing law on vehicle registration, you should check the exact requirements within your country.