Sql-server – Can the replicated database be the publisher with SQL Server

If you truncated the table on the publisher the record in the transaction log would be an insert, and therefor an insert would be executed against the subscriber.

Now what you can do is modify the stored procedures that replication uses at the subscriber so that when the insert procedure fires it first looks to see if the record exists and if it does it does an update, and if it doesn't it does an insert.

Is there anything to modify on the the copied database to make the publisher reconise it as the deleted one and continues synchronizing ?

This is not possible. The subscription is now broken and should be removed / recreated per your requirements. There are unique identifiers in play beyond the DB name which is why it didn't work as you intended.