Attempted regex:

$pattern = '#</ListItem>\s*<BulletList>(.*?)</BulletList>#s';
$bulletlist = preg_replace($pattern, "<BulletList>\\1</BulletList></ListItem>", $bulletlist);


Input data:
<?xml version="1.0" encoding="utf-8"?>

<BulletList>
 <ListItem>Ut pellentesque nunc gravida odio.</ListItem>
 <BulletList>
  <ListItem>Aliquam fermentum neque ut risus.</ListItem>
  <ListItem>Suspendisse elementum nunc nec libero.</ListItem>
  <ListItem>Fusce vehicula imperdiet urna.</ListItem>
  <BulletList>
   <ListItem>Curabitur tempus metus vitae dolor.</ListItem>
  </BulletList>
 </BulletList>
</BulletList>


Actual output from above regex:

<BulletList>
 <ListItem>Ut pellentesque nunc gravida odio.<BulletList>
  <ListItem>Aliquam fermentum neque ut risus.</ListItem>
  <ListItem>Suspendisse elementum nunc nec libero.</ListItem>
  <ListItem>Fusce vehicula imperdiet urna.</ListItem>
  <BulletList>
   <ListItem>Curabitur tempus metus vitae dolor.</ListItem>
  </BulletList></BulletList></ListItem>
 </BulletList>


Needed output data:

<BulletList>
 <ListItem>Ut pellentesque nunc gravida odio.<BulletList>
  <ListItem>Aliquam fermentum neque ut risus.</ListItem>
  <ListItem>Suspendisse elementum nunc nec libero.</ListItem>
  <ListItem>Fusce vehicula imperdiet urna.<BulletList>
   <ListItem>Curabitur tempus metus vitae dolor.</ListItem>
  </BulletList></ListItem>
  
 </BulletList></ListItem>
 
</BulletList>