Scoop up the remains. We use disposable clear cups. Get as much of the egg cleaned up as possible. You may have to scrap the nest box or where ever the egg is.
Take the time to evaluate the egg. Was the shell soft? Was the nest crowded with eggs? Is there enough nesting material?
LOL, out of my 6 hens, only 2 use the nesting boxes...the others plop 'em out on the floor...seems they always scratch the bedding away first, too! We put down plastic (it's sort of made like cardboard, but it's plastic) and haven't had any break yet. In the nesting box, we put in a piece of that plastic mat that's meant to be a door mat...it's got little spiky things so it gives the egg something to rest on. When it gets really gucky, we take it out and hose it off. One of the girls climbs in the box and scratches all the bedding out before she lays and the other gets in and picks certain pieces of straw and puts 'em in. Go figure! LOL
My nesting boxes are lined with wood shavings and my girls always manage to scratch them down to the wood floor. It is possible that when one of them was getting in it it could have landed on it and cracked it. I have had a few cracked. I could possibly be that the shell of the egg are too week. If the shells are really thin then it could be that someone could have stepped on it. If the shells are thin try adding some oyster shell or egg shells to their diet. They may be lacking calcium.
Thats a great idea to use the plastic mats! I had 2 cracked eggs when I picked them up today and wasnt sure what to do about it. We use the wood shavings also and have the same problem with the chickens pecking and scratching the shavings out. Have to get some mats this weekend!
I can't claim credit for the idea; I saw it posted here on BYC somewhere, and we happened to have one that was old and kinda beat up so we used that and so far, it's worked great! There's rarely much bedding in the box and they can't scratch the mat out so it seems to do just what we need it to do!