You can do either with a blockchain fork - forkers tend to copy the chain because their intention is to carry existing assets to the new chain. But there is no technical need to do so.
With Safecoin I suspect that datachains will make it possible to replicate the data, and therefore Safecoin holdings, on a new fork so again it would technically possible to do either.
As the size of SAFEnetwork grows it becomes harder and harder to bootstrap a network that replicates SAFEnetwork in all respects, but still feasible to carry across Safecoin and other selected data types because the space needed to store these will be relatively insignificant (less than a blockchain with years of transactions for example).
This doesn’t invalidate your question, other than to say I don’t believe it discriminates between blockchain and Safecoin, or other SAFE cryptocurrencies. But since it is just a choice which would be made based on circumstances, I’m not sure the answer is useful without a specific case to consider.