Depending on the restrictions you put on the answer, it could be

-9999 (least 4-digit number if negative numbers are allowed)

0000 (least if leading zeros are allowed, but not negative numbers)

0001 (least if leading zeros are allowed, but must be positive)

1000 (least if only positive numbers with no leading zeros are allowed)

-9999 (least 4-digit number if negative numbers are allowed)

0000 (least if leading zeros are allowed, but not negative numbers)

0001 (least if leading zeros are allowed, but must be positive)

1000 (least if only positive numbers with no leading zeros are allowed)