Exempting sunday from oracle sql script

Kindly help me check the script below

SELECT CASE
       WHEN to_char(sysdate - 1, 'DAY') = 'SUNDAY' THEN
          trunc(sysdate - 2)
       ELSE
          trunc(sysdate - 1)
       END AS day
  FROM dual

I wish to return 2 days if the condition in the case is true else to return previous day but the script keeps returning the previous day

To remove all language-dependencies you can use TRUNC(SYSDATE - 1) - TRUNC(SYSDATE - 1, 'IW') to count the number of days since the start of the iso-week (which is always on a Monday):

SELECT CASE TRUNC( SYSDATE - 1 ) - TRUNC( SYSDATE - 1, 'IW' )
       WHEN 6                                                 -- Sunday
       THEN TRUNC( SYSDATE - 2 )
       ELSE TRUNC( SYSDATE - 1 )
       END AS day 
FROM   DUAL

db<>fiddle

When you use TO_CHAR(sysdate-1,'DAY') then result is padded with spaces. Try SELECT '"'||TO_CHAR(sysdate-1,'DAY')||'"' in order to see the effect.

Use Format Model Modifiers FM and you should define also the language explicitly:

TO_CHAR(sysdate-1, 'fmDAY', 'NLS_DATE_LANGUAGE = American') = 'SUNDAY'

or

TRIM(TO_CHAR(sysdate-1, 'DAY', 'NLS_DATE_LANGUAGE = American')) = 'SUNDAY'

Use DY -- it is always 3 characters:

SELECT (CASE WHEN to_char(sysdate - 1, 'DY') = 'SUN' 
             THEN trunc(sysdate - 2)
             ELSE trunc(sysdate - 1)
        END) AS day
FROM dual;

To be formally correct, you should include an NLS parameter as the third argument ('NLS_DATE_LANGUAGE = American') to be sure that the results are in English.