If he had done the backup, then he would be able to do an incomplete recovery on the database using the until cancel option as you mentioned. The commands that I mentioned is applicable to the all the logfiles with the status INVALID/STALE/Blank (i.e. the file is in use)

Code:
     Please do the following and post us the result:

         SELECT * FROM v$log;
          
         SELECT * FROM v$logfile;
To better undestand the problem.
Sam