Normally a face-down permanent is a 2/2 creature with no name, color or any other characteristics. So what happens if an effect makes it a copy of something else?
Quite many players, even very experience ones, will intuitively say that it simply becomes a copy of that something else (ie. in this case it will become an exact copy of Llanowar Elves, ie. a 1/1 green creature with that name, and with its ability.) Their intuition will usually be less sure about the question of what happens to its original morph ability, and whether it can be morphed or not. Some will guess that it retains its morph ability and can be morphed, but once morphed it will still be a copy of Llanowar elves.
Of course it's not that simple, and the situation is a bit more curious.
What actually happens is that it's the down-facing side (ie. the front of the card) of the permanent that becomes a copy of Llanowar Elves, not the up-facing side. The permanent will still be a 2/2 creature with no other characteristics even though it's now a copy of Llanowar Elves.
Since the down-facing side has no morphing ability now, it can't be morphed (for as long as it remains a copy of Llanowar Elves.) If Mirrorweave had instead targeted some other creature with a morph ability, then you could morph your face-down creature using the morph cost of that other card (if you can pay it.) However, when it turns face up, it will still be a copy of that other card.
The face-down permanent could even become a copy of a non-creature (for example if Mirrorweave had targeted an animated land.) While the down-facing side would become a copy of that non-creature card, it would still be a 2/2 creature with no other characteristics.
The reason for this is that being "face down" is a state of the permanent in the exact same way as being tapped or phased out. Being in the "face-down state" implicitly means that the permanent is a 2/2 creature with no other characteristics (regardless of what the actual card is.) It would work even if a permanent, like a land, would somehow become turned face down by some effect: It would become a 2/2 creature regardless of what it originally was.
However, note that copying in the other direction is special. In other words, if Mirrorweave had targeted the face-down permanent, then every other creature would have become a 2/2 creature with no other characteristics (rather than a copy of Willbender.) This is because the rules of the game specifically define the mechanic to work like that. (More exactly, the rules state that the visible characteristics of the face-down permanent, ie. "2/2 creature" become its copyable values.)
