Do you have a cite for that? Either part?
Not many graves of crucifixion victims have been found, but one suggests they would be buried with nails still in them, if in fact they were buried at all.
From Wikipedia:
The terms you should be searching for are Stipes (the permenant or semi-permenant upright post) and the Patinulum (the crossbeam).
As for the nails, the only times I can see that they are left in the body is when they are bent in a way that prevents them from being removed. From your own link:
Iron was EXPENSIVE! Remember that this is an era where people were constantly ripping apart older buildings to use their components to make new buildings (which leaves archeologists with only scraps).
Were crucifixion nails necessarily iron?
They weren’t always nails, often people were just tied to the cross.
But if you WERE going to use nails, I think they probably did have to be iron. I’m not sure that a couple of copper nails would successfully penetrate all the way through a limb without deforming when hitting bone, and I’m not sure that they’d be able to hold up a human body. I think copper nails are only meant to hold up a few pounds.
And anyways, the Romans used iron for construction, so it would have been available; copper nails were only used for decorative ornaments and for ship building.
Something for Mythbusters to test?
Also, on an unrelated note, whenever I see the thread title I wonder what the acronym NOAH stands for 
I was thinking more bronze than copper. But I’ll admit to very little experience with non-ferrous nails, and even less experience at using them for crucifixion.
It’s never too late to pick up a new hobby! You can teach an old dog new tricks!
Given the rest of this thread I think the uppercase acronyms (both of them) stand for:
National Organization of Amateur Historians - Ararat Research Klatsch
You know, the sub-group of guys who keep making stupid Discovery-style videos about supposedly expeditioning out to find an Ark when they could be showing us scenes of a hole dug in their backyard for all we know.
Crucifixtion’s a doddle.
Is this the origin of hockey?
By finding the crosses in the right area- then testing the three crosses by a miracle. Like i said-
But in any case- the Cross found and the few bits remaining (they lost the Cross in a debacle battle during the Crusades) are legit relics of St Helena.
Not cheap, sure, but not that precious-
https://www.academia.edu/12975842/Horrible_Speculative_Nasty_Dangerous_Assessing_the_Value_of_Roman_Iron
- Iron’s price at Vindolanda was approximately 1.1 denarii per kilogram in early second century A.D.
Bronze was much more expensive.
Nautical Overburdened Animal Handler
Finding the Patinulum? Or the Stipes? Or both? The Romans were crucifying people in that area for hundreds of years, wouldn’t we expect to find lots of remnants from crosses in 300 AD?
And how exactly does one do that? 
Yes, it was a common method of execution. Lots and lots of people killed that way. Although, i suppose if they usually reused the uprights, the odds of finding a piece that was used for a particular execution are a lot higher. Still, 300 years later, I’m pretty sure they would have had to swap out the uprights a few times. The originals were no doubt either burned or turned into a doorway or something somewhere else.
The latter part of your sentence firmly establishes that those involved were fervent religious fantasists and unreliable narrators; such that their claims related in the first part of your sentence are IMHO to be treated as having no truth value.
Or to be blunt - we know by their own words they were liars so why on earth do you believe them?
I think you’re missing the correction @DrDeth issued:
Are they verifiable (in any non-religious sense) relics of the True Cross? Unknown, he has his doubts. There is better provenance though to consider them valid relics of St Helena.
Not having the information or inclination to try to find the chain of custody on said “few bits remaining” but it’s likely at least more plausible given semi-continuous custody rather than the 300 year gap between when the fragments of the True Cross were found by “miracle”.
Exactly. I have doubts that cross was really the one Yeshua ben Joseph was executed on. But it is doubtless the one St Helena found, thus the few bits remaining are indeed Relics of a Saint.
I’m not missing anything. The established (by her own tale) facts are that St Helena was a liar and or idiot.
I don’t see any reason to believe anything she is reported as saying or doing. That she found wood where she said she did. That she even necessarily went where she said she did. That what she found was remains of a crucifixion cross. These religiously fervent people are absolutely full of shit. If they told me the sky was blue I’d begin to doubt it. There is no reason to believe anything at all of her tale, or the tales told about her.
It is absolutely beyond me as to why anyone would use the word “doubtless” within a million miles of a person known to be a religious fantasist and liar.
I am very sure she was not lying. Yes, she was deeply religious, but I am certain she believed those were the crosses- two for thieves and one for Christ, and that she sincerely believed her test worked.
You can be very very certain of something and still be completely wrong.
Even assuming you are correct that she was a fantasist not a knowing liar, that doesn’t mean that any part of the tale is true.