Эмулировать папку /proc

С GNU Awk (gawk ), который поддерживает многомерные массивы, логика выглядит так:

gawk '
  NR==FNR {
    a[$2][++c[$2]] = $1; next
  } 
  $2 in a {
    for (i in a[$2]) 
      print $1 " is dependent on " a[$2][i] " for " $2
  }
' File1 File2
"BRGTEST-244" is dependent on "BRGTEST-242" for a.txt
"BRGTEST-244" is dependent on "BRGTEST-240" for a.txt
"BRGTEST-221" is dependent on "BRGTEST-219" for e.txt

Если нужно убрать и кавычки:

gawk '
  NR==FNR {
    a[$2][++c[$2]] = substr($1,2,length($1)-2); next
  } 
  $2 in a {
    for (i in a[$2]) 
      print substr($1,2,length($1)-2) " is dependent on " a[$2][i] " for " $2
  }
' File1 File2
BRGTEST-244 is dependent on BRGTEST-242 for a.txt
BRGTEST-244 is dependent on BRGTEST-240 for a.txt
BRGTEST-221 is dependent on BRGTEST-219 for e.txt