Yes he can apply for grace marks in the subject which you had mentioned if he clears the other backlogs left over. Can you mention whats the backlogs left over from 1 to 4 years & to which year/semester does those backlogs belong to ? So, that i can give a proper suggestion to get the memos soon. Mention course & regulation even.
B.Tech Students are having an option to leave 2 subjects & they even can apply for grace marks.