I have had chicks that were taking a long time to hatch get so dried out that it looked like they were shrink wrapped! I have had to wet my finger in warm water and rub until their wings unglued them selves from across the eyes. It looked like what's left on the plate after you eat eggs sunny side up and leave it in the sink without rinsing!
The poor chicks end up looking like the god of hair gel got really mad and took it out on them, but as long as all the moving parts (and orifices!)were freed up, I just left them and within a week or so, they had preened themselves to normal appearance.
Sometimes it's the white outer membrane that is really tough and dry and sometimes the inner gooey/gluey one.