I'm not sure what setup you've got in your engine, Gnekker, we don't use a
1.6 in the 2003 Elantra in the U.S. Presuming it's the basic beta design,
yes, eventually they could clog to the point of severe engine damage.
It sounds to me like no one has actually identified the cause of the
problem in your engine. I've seen it caused by grit in the oiling system,
by faulty lifters, by insufficient oil pressure (for several reasons), or
by clogged oil passages.
If it's just the rocker arms that are clogged, you'd be looking at several
hundred U.S. dollars to clean out. If it's worse than that and has invaded
the passages in the head and block, then you're looking at thousands of
U.S. dollars to remove the head/block and send to be hot tanked. But I
have no idea what labor costs are in your corner of the world.