If it's a really long split like this one, apply a little wad of cotton from a Q-tip about the size of a match-head to the wet CA; add another drop and press the excess out with a flat of a knife. The fibers will reinforce the CA enough that the nail can grow out before the CA "blowout patch" fails.
Those without experience of this beware - the reaction between cotton and cyanoacrylate can be highly exothermic. It's one thing for it to get hot, it's another for it to get too hot when it's firmly glued to your person!
Fibreglass tissue is a better choice than cotton, if you have some handy. (I keep small quantities of fibreglass tissue, carbon fibre fabric and Kevlar felt in my 'gluing things' box precisely so that I do have such things handy. Small quantities can be picked up for a very little money from the EvilBay and the usual scumbags.)
Oh, FFS... There's a reason why
I specified a bit the size of a match-head. That small amount will not generate any appreciable amount of heat. Also why I specified "from a Q-tip"; as it will be 100% cotton, not cotton-poly blend or other synthethic fibers. Even the entirety of a Q-tip saturated in CA is not going to be thermally hazardous (though the vapor thereof can do a number on your mucous membranes & eyeballs if they get too close), unless there's some reaction with the stick.
Fiberglas, in contrast, is considered a hazardous material for many reasons; particularly in loose-strand or bundled into a tow as is commonly used the way you suggest. I prefer to NOT use it to patch myself up. My boats, cars, aircraft and even my home, yes. But NOT my person.
mnem
"Better living through chemistry."