Finalmente
virt01@virt01:~$ sed 's/_0*$/_00001/g' some.txt
somestring_oooo_00001
somestring_oooo_00001
somestring_oooo_00001
virt01@virt01:~$
Exatamente para seus dados
virt01@virt01:~$ cat some.txt
FOO_AAAAA_00001
FOO_BBBBB_00001
FOO_ABABAB_0000
FOO_ABCCDAA_00
FOO_12345678_0
FOO_JJJ_00001
FOO_VLLLL_00001
FOO_KKAKAA_00001
virt01@virt01:~$ sed 's/_0*$/_00001/g' some.txt
FOO_AAAAA_00001
FOO_BBBBB_00001
FOO_ABABAB_00001
FOO_ABCCDAA_00001
FOO_12345678_00001
FOO_JJJ_00001
FOO_VLLLL_00001
FOO_KKAKAA_00001
virt01@virt01:~$
Espero que ajude.