InnoDB - Use combined index with primary key on GROUP BY
Because you only select columns from table_1 and because table_2 is only joined (on the right side) of the LEFT JOIN and none of its columns is used elsewhere (SELECT, WHERE, GROUP BY or ORDER BY clauses), you can completely remove the LEFT JOIN table_2 t2 on t1.id = t2.refid part.

This might have given less rows in the result but because you group by the Primary key of table_1 after the join, there is no such case.

SELECT t1.a 
FROM table_1 t1 
WHERE t1.b = 99
GROUP BY t1.id
ORDER BY t1.c ;


Now, because you group by the Primary key of table_1, which is redundant when you have only one table, you can also remove that part: GROUP BY t1.id 

Finally, the query is equivalent to:

SELECT t1.a 
FROM table_1 t1 
WHERE t1.b = 99
ORDER BY t1.c ;


which should use the index on (b, c), which yes, includes the primary key. You may consider it to be (b, c, id) if you want.

But whether that index will be used is not 100% sure. Depending on the selectivity of column b (what percent of the whole table has b=99?) this index may or may not be used. If there a lot of rows with b=99 (a large percentage), the optimizer may choose to scan the whole table instead and do a filesort, than use the index, select those (99,c) combinations that exist and then hit the table to find the a values.

If you have an index on (b, c, a) or on (b, c, id, a), the query will be able to find all the info that is needed in this index and in the correct order, so it will use it.