Here's a simple change to get what you want... notice that I simple "add" that text back...

=IF(ISNUMBER(SEARCH("NonEmp",A1)),SUBSTITUTE(RIGHT(A1,LEN(A1)-FIND(",",A1)-1)&" "&LEFT(A1,FIND(",",A1)-1)," (NonEmp)","")&" (NonEmp)",IF(ISNUMBER(SEARCH("Non Emp",A1)),SUBSTITUTE(RIGHT(A1,LEN(A1)-FIND(",",A1)-1)&" "&LEFT(A1,FIND(",",A1)-1)," (Non Emp)","")&" (NonEmp)",RIGHT(A1,LEN(A1)-FIND(",",A1)-1)&" "&LEFT(A1,FIND(",",A1)-1)))