Welcome to the forum! Lots of unknowns here, so try to bear with me and my questions, lol...
First of all, what species of "parrots" are we talking about here? If I just missed where you mentioned that, then I apologize, I didn't catch it.
How much experience do you have hand-raising and/or hand-feeding baby birds under normal circumstances (meaning pulling eggs between 2-3 weeks old, raising them in a Brooder, and hand-feeding until they are Abundance-Weaned)? I'm assuming you know all about the necessary Ambient temperatures, necessary formula temperatures, feeding schedules, etc.?
Do you have experience Abundance-Weaning baby birds?
You mentioned that in addition to destroying the eggs, they also sometimes eat them...This tells me right away that your birds may very well be Calcium deficient, specifically your female, as it's very common for them to eat the eggs after laying them if their bodies do not have a high-enough level of Calcium to produce the eggs. Make sure you have both a Cuttlebone and a Mineral Block in with the breeding pair, and if you already do have both in with them, then I'd definitely either buy a bag of Egg-Food at the pet shop, or just make your own Egg-Food, which contains the shells ground up and mixed in, and make sure that they always have access to a dish of it before, during, and after laying a clutch.
Also, when a female or both parents (depends on the species of bird) allow an entire clutch of eggs to be laid, then they lay on the eggs for a time period and then start destroying the eggs, and this happens repeatedly, again, it's an indication that SOMETHING isn't quite right...This could be that they are calcium deficient, it could be a problem in their environment, it could be that they think that there is something wrong with the eggs or the chicks inside, something isn't proper for them to want to have babies hatch and be raised. So a little more information about their habitat/environment/daily diet, etc. might provide some insight...As already mentioned by Noodles, if you haven't had at least the female to a CAV or Avian Specialist within the last year and had routine blood-work done on at least her (should be both birds, but the female's blood work is a must), then I highly suggest that you do this BEFORE trying to breed them again. Not only do you always want to ensure that your birds are healthy enough to breed/lay eggs/raise chicks for the first 2-3 weeks, the blood work also may tell you right away why they are destroying the eggs. It could be that simple.
****As a parrot breeder/hand-raiser/feeder of 20 years who grew-up with a grandmother and mother who also bred for decades, I can tell you that I would never, ever even consider pulling a chick before it's 2 weeks old and trying to hand-feed it. There are a bunch of reasons why I say this (the fact that they die 95% of the time basically encompasses my reasons, lol), but the main reasons are #1) The parents do in-fact feed the babies much-needed "crop milk", for a lack of a better term to call it, it's not actually "milk", but the babies do get antibodies and antigens from the parents for the first 2-3 weeks of life, and you're depriving them of this if you don't allow it to happen, and #2) The odds of a baby you raise from hatching developing correctly, even if they do survive, are very high. They tend to be undersized and have developmental issues...And of course, the chances that you will aspirate a baby that is less than 2 weeks old is as high as it can be without it being 100%...And they die instantly when this happens, literally instantly, and if you've never had this happen to you before, let me tell you how absolutely devastating it is to experience. I had it happen one time, years ago, to a Budgie chick that was perfectly happy and healthy, and just 3 weeks old. It was just a freak thing, and they are so small they literally have a little bit of a "seizure" type of attack and fall over dead in your hand. It's awful. And the odds of this happening to a newly-hatched little baby, well, they're pretty good. And also, they can of course aspirate a little formula if they are a larger species of parrot (I don't know what you're breeding here), develop pneumonia, and suffer and then die, and it's drawn-out over a week instead of instantly...So it's just not something that I would ever do, and certainly not recommend to anyone.
There are a lot of things that you can do to knock your birds out of breeding-season and to stop them from breeding and laying eggs in the first place, so if what you said was true and you just don't want the fertile eggs to be destroyed, and that's why you're thinking of doing this, I'd actually just recommend that you work on just getting your female out of breeding season and to stop laying eggs in the first place. It's better for her health overall, and it solves the issue at hand...
