Italian Greyhounds can break legs. It is important to remember the majority of leg breaks are from "puppy accidents" and while IGs shouldn't live a secluded life, care must be taken to make sure they are not doing dare-devil stunts that could result in injury (such as jumping from high places... like off the back of sofas, tables, porches or balconies).
Accidents do happen, however, and always at such inconvenient times. There is nothing like the scream of an Italian Greyhound when a leg breaks. It is a sound that cannot be missed! The first thing to do is to calmly pick up the hurt IG (and watch out for a possible dog bite!) Then call a vet immediately. Upon consultation and examination of the broken leg by a vet...be sure to follow the advice carefully. Follow through with all veterinary directions. (Note: in preparation for the possibility of a leg break it is a good idea to consult with a vet upon purchase of the dog. Ask about leg breaks and learn about the use of a spoon splint. Obtaining this knowledge ahead of time and having this splint already available in the home may prove very useful. While one would hope to never have to deal with a broken leg this prior work could pay-off!)
The important thing to remember with all leg breaks is that in order for the leg to heal, the dog MUST be confined. As broken legs seem to occur more often in puppies this can be a very hard line to follow. Whining puppies who want to play can wreak havoc on an owner's heart. But stand firm! Do not allow a puppy with a broken leg to run around. Keep the cast dry and follow the vet's recommendations on the number of times it is to be changed. Keep an eye out for any possible sores on the leg. Crate rest can be important and having an exercise pen can be a big help in the process of healing. These pens are big enough for dogs to move yet small enough to keep them from further damaging the affected leg. Do not allow a puppy to jump up and down nor run around while in a cast. The more the puppy moves, the longer it will take for the leg to heal.
Once the cast is off, remember... the leg will need time to rebuild muscle. Any leash training prior to the leg break will reap a reward at this time. Controlled exercise can slowly help the dog to rebuild strength in the leg. I recommend to allow at least four weeks after the cast is removed before letting a puppy return to normal play routines (such as running, jumping, etc). The work that is put into rebuilding muscles will pay off in the long run. As always, follow the veterinarian's advice.