select * from(
   (select * from messages where '$usr'=sender
      order by date desc limit 1)
   union all
   (select * from messages where '$usr'=receiver
      order by date desc limit 1)
   )u

select * 
from messages mm
where mm.id in
(
select max(id) max_id, if(m.sender='abc',m.receiver,m.sender) abonent
from messages m
where m.sended = 'abc' or m.receiver = 'abc'
group by abonent
)

select * 
from messages mm
where mm.id in
(
select 
  max(id) max_id
from 
(
  select m5.id, m5.receiver abonent
  from messages m5
  where m5.sender = 'abc'  -- по индексу
  union all
  select m6.id, m6.sender abonent
  from messages m6
  where m6.receiver = 'abc'   -- по индексу
) mmm
group by abonent
)