To unload all the rows from a table into one or more files in a named stage, the correct command to use is 'COPY INTO'. This command copies the contents of a table into files within a specified stage. It does not insert data into a table (which is what 'INSERT INTO' does), retrieve data from a stage to the local machine (as 'GET' would), or upload files to a stage (which is the function of 'PUT'). Therefore, 'COPY INTO' is the appropriate command for unloading data from a table to a stage.