I can run through a DNA scenario. I got my Ph.D. working with archived samples up to 100 years old for evolution studies. In fact, I got my Ph.D. in the lab where PCR was developed and was the first generation of young researchers to use the tool. It's an area I know something about.
You're 88 years old and your child has been missing for 42 years. You've come to terms with the loss of your child by now but of course it still hurts.
Someone comes and asks for some hair, for example. It's the only thing you have to remember your child by, but sure, you give it up to get some DNA. There needs to be actual tissue attached to the hair to get that DNA. It can't just be cut off and kept in a box for sixty years. But say by chance there's a hair or two that has tissue attached. Great. DNA degrades over time and due to conditions but say the box of hair has been kept in dry, dark conditions, and no moisture has come in to create chemical conditions that degrade DNA. It's not a museum archive or a tissue storage facility but again, by chance one of the follicles has extractable DNA and it provides fragments large enough to fingerprint. Those seeking closure for the parents (something they're not asking for, by the way, they've reconciled and gone through their stages of grief) get what they want.
The DNA is sequenced, the family sits on pins and needles for a while, the whole thing having now become fresh in their minds like it was yesterday.
Most likely scenario there's no match.
However there's always a chance and EUEKA....a Jane Doe from sometime over the last 40 years is a match.
What does the family get out of this? They get to see photos of their dead daughter lying on a slab. Great. They've been remembering their daughter as a happy and beautiful child and young woman, now that vision is replaced by a bloated, beaten and tortured body on a slab. 'Cause you know if she was killed she wasn't killed easy. She was a young woman abducted and disappeared.
Another scenario, she's been in the desert in a ditch for 40 years and they get a bag full of bones. GREAT. Same scenario as above.
The only thing they get out of this is that they get to have a funeral. Do they want this? Do they need this? Has anybody asked? Do we even know that the family has been asked for a DNA sample? This is a cold case. Nobody's picking it up; a couple of us have gone that route and found that out.
One positive outcome could be that justice could be done. It's their daughter after all, maybe they want that. However, even if they get an I.D. the chances of finding the people who did it to her are close to nil. What's left of say hair or skin from the perps after 40 years of lying in a ditch in the desert?
My point here is I'd tend to be easy on the parents. It's most likely not even a matter of them refusing to provide DNA samples. It's a cold case and had been a cold case for more than a decade before DNA methods had even evolved to the point where they were used regularly for fresh cases. Those of us who have tried to get the police to look at the case again don't even get a response.
And, I'd hope that anybody who doesn't have a solid reason for asking for DNA would think about the possible outcomes for the parents and family and what THEY want and need before doing that asking.