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A female bird can and does lay eggs without fertilization occuring. The eggs won't result in hatching unless there was/is a male available to fertilize them. If the male has been absent for more than about 8-10 days prior to the egg laying, these eggs are not likely fertile.
Here is a lot more about Zebra Finches http://animal-world.com/encyclo/birds/finches/ZebraFinch.php
HelloCustomer Even though it sounds like your girl will not be having any chicks from those eggs, it's just as important that she be getting a good varied diet that has all the nutrition she needs. Egg laying can be stressful times on the health of a female bird, regardless of whether the eggs are fertile or not. She is calling heavily on her calciuim reserves to make strong shells for those eggs and if she should run low on calcium, she could be in a medical emergency before you even realize it. Without enough calcium, her shells will be too soft for her to pass. She can become eggbound, or worse. Worse would be if an egg should rupture inside of her or if she should strain so hard trying to pass it that she suffers a prolapse of her uterus. Either of those is life threatening so please check out these links about proper diet and if you have any more questions at all, just let me know. Patricia
Click here: Egg Binding and Chronic Egg Laying
Click here: The Finch Niche - Finch Information & Articles by Myra - Breeding Zebra Finches
Click here: Zebra Finches
In addition, there is : http://www.zbirds.com/Breeding.html A comprehensive site you will certainly find helpful - along, of course, with this one and a team of people working together for the benefit of healthy pets and happy owners.