@Gary_W has written about the problem with using that regex pattern to split strings, precisely because of how it treats empty tags. (And is on a mission...)
The alternate approach in that post works here too, with the pipe delimiter escaped:
with t (str) as (
select '1|CAT|DOG' from dual
union all select '3|HARRY|GOAT|STACK' from dual
union all select '6||LION|TIGER' from dual
)
select str, regexp_substr(str, '(.*?)(\||$)', 1, 2, null, 1) from t;
STR REGEXP_SUBSTR(STR,
------------------ ------------------
1|CAT|DOG CAT
3|HARRY|GOAT|STACK HARRY
6||LION|TIGER
Similarly for the third element:
select str, regexp_substr(str, '(.*?)(\||$)', 1, 3, null, 1) from t;
STR REGEXP_SUBSTR(STR,
------------------ ------------------
1|CAT|DOG DOG
3|HARRY|GOAT|STACK GOAT
6||LION|TIGER LION
And the fourth:
select str, regexp_substr(str, '(.*?)(\||$)', 1, 4, null, 1) from t;
STR REGEXP_SUBSTR(STR,
------------------ ------------------
1|CAT|DOG
3|HARRY|GOAT|STACK STACK
6||LION|TIGER TIGER