Copy line and insert it in a new position with sed or awk

With ed:

$ printf '$t0\n,p\n' | ed -s file
f
a
b
c
d
e
f

The t command in ed transfers/copies a line from the addressed line (here $ for the last line) to after the line addressed by its argument (here 0, i.e. insert before the first line). The ,p command prints the contents of the editing buffer (change this to w to write the result back into the file).

or simply like this, without sed or other

tail -1 list && cat list

Pure sed:

sed 'H;1h;$!d;G' file.txt

All lines are collected in the hold space, then appended to the last line:

• H appends the current line to the hold space. Unfortunally this will start the hold space with a newline, so 1h for the first line, the hold space gets overwritte with that line without preceeding newline
• $!d means if this is not (!) the last line ($), delete the line, because we don't want to print it yet
• G is only executed for the last line, because for other lines the d stopped processing. Now all lines (first to last) we collected in the hold space get appended to the current (last) line with the G command and everything gets printed at the end of the script.