$d = 0;
$sql="SELECT * FROM  emplyeelist WHERE StatuseUnder = '$EmpIdSE'";
$result = mysqli_query($db,$sql);

while($row = mysqli_fetch_assoc($result)){
    echo "$row['fullName']"."<input type = 'Checkbox' name = 'EmpName[$d]' value = '".$row['fullName']."'>";
    ++$d;
}
$size = count($_POST['EmpName']);
$d = 0;
while ($d < $size){
    $EmpName = $_POST['EmpName'][$d];
    $sql = "INSERT INTO ...";
    $result = mysqli_query($db,$sql);
++$d;
}

<?php
$d = 0;
$sql="SELECT * FROM  emplyeelist WHERE StatuseUnder = '$EmpIdSE'";
$result = mysqli_query($db,$sql);
while($row = mysqli_fetch_assoc($result)){
echo "<input type = 'text' readonly name = 'EmpName[$d]' value ='".$row['fullName']."'>".
"<input type = 'checkbox' readonly name = 'CheckBoxEmpName[$d]' value = '".$row['fullName']."'>"."</br>";
++$d;}
 ?>

$d = 0;
while ($d < $size){
$EmpName = $_POST['EmpName'][$d];
$CheckBoxEmpName = isset( $_POST['CheckBoxEmpName'][$d]) $_POST['CheckBoxEmpName'][$d] : "";
if(!empty($CheckBoxEmpName)){
$sql = "INSERT INTO  table_name (table_row_name)VALUES ('$EmpName')";
$result = mysqli_query($db,$sql);
}++$d;}