The Postgres function drops the attribute value and checks constraint violation if the row contains the attribute value.

enum_attr_drop.sql

ALTER PROCEDURE enum_attr_drop OWNER TO {delete role for pg_enum};

CREATE OR REPLACE PROCEDURE enum_attr_drop(inType varchar, inAttr varchar)
   LANGUAGE PLPGSQL
   SECURITY DEFINER 
AS $$
declare
isBind RECORD;
dQuery varchar;
hasRecord bigint;
errMsg varchar;
begin

    if inType is null or inType = '' or  inAttr is null or inAttr = '' or  then
        raise exception query_canceled;
    end if;
   
	FOR isBind IN SELECT t.table_schema
   						, t.table_name
   						, t.column_name
  					FROM information_schema.column_udt_usage t 
  				where t.UDT_NAME = inType
  	LOOP 
	  
			SELECT format('select count(1) from %s.%s t where t.%s = ''%s'''
						, isBind.table_schema
						, isBind.table_name
						, isBind.column_name
						, inAttr) into dQuery;
			
  		EXECUTE dQuery INTO hasRecord;
			
			IF hasRecord > 0 THEN
				errMsg := 'Relations found "' 
					||  isBind.table_schema 
					|| '.' 
					|| isBind.table_name 
					|| '.' 
					|| isBind.column_name 
					|| '" by type value ' 
					|| inAttr;
		  		raise exception foreign_key_violation;
		  	END IF;
	  
  END LOOP;
  

    delete from pg_enum
 		where enumtypid=inType::regtype
   		and enumlabel=inAttr;

    exception
        when no_data_found then
            raise exception no_data_found
            using hint = 'Not found attribute ' || inAttr || ' in type ' || inType;
        when query_canceled then
            raise exception query_canceled
            using hint = 'Param inType or InAttr is null or empty';
		when foreign_key_violation then
            raise exception foreign_key_violation
            using hint = errMsg;
        when invalid_text_representation then
        	raise exception invalid_text_representation
        	using hint = 'Attribute ' || inAttr || ' is not found in type ' || inType;
        
end;
$$;