Can a check be destroyed or does it have to be returned to the person

I sent a check for a partial payment of a debt to a lawyer. They now have requested I send them one check for the entire amount and once they receive that in-full check, they will destroy the partial check. Can they destroy it or does it have to be returned to me?

My revised, bottom-line advice: offer to send a 2nd payment (preferably in the form of money order or cashier's check) for the difference you are agreeing to pay. I cannot imagine any reason why they would object to this - there is no fee to cash a check, there's less risk of error, and less work involved. Alternatively, offer to send a new check only once the other has been returned. Don't issue one more full-amount check while the other is still outstanding.
There is a good reason not to accept partial payment by them, which is that accepting a partial payment of a debt comes with a varieties of strings attached depending on the nature of the debt (such as with evictions, court processes may need to be restarted, etc). They likely want to avoid such a situation - but this does not provide any support for why they can't just take a second payment and then cash it all at once as a single, full settlement of the debt.

In a perfect world, you could skip all the non-sense by simply having your bank put a stop-payment on the old check before sending a new one. Unfortunately, this might not work with 100% accuracy - but in your case if the "partial payment" is a significant amount of money to you, I'd go ahead and spend the $20-40 to put in the order now as an extra safety on them not doing what they claim, if for some incredibly stupid reason you can't handle this with a 2nd payment instead of one single full one.
It turns out banks have lots of surprising and stupid rules, like stop payments on a check expiring in 6 months (and they may even cash stale checks over a year old), no guarantee of a stop being successful, etc. The real rule is: they might cash the check unless you close the account. Sigh - this is one of many reasons I never, ever use checks.

I am not aware of any law that requires a check to be physically returned if requested, or proof or destruction provided, or anything like that. It's a large part of the reason why we have the ability to stop payment on a check, and so void it through the bank without having any physical access to the check - but this process is spotty and imperfect, and cannot be relied upon.
You can request them to do whatever you like, like void it and send it back, or destroy it, and they can just refuse - or say they'll do it and then just not do it, and you have no real useful recourse.
The main goal should be to avoid losing money if someone "accidentally" (or intentionally) cashes both checks. So you can ask, or demand (refuse to pay until they return the check), etc - and they can respond more or less any way they want.

As a final piece of future advice, consider no longer using checks for purposes like this. Switch to using something like a cashier's check or money order offered by your bank, which (by their very nature) takes the money out of your account immediately, severs all ongoing connection to your bank account, and is effectively like cash with the added benefit of a paper trail. Keep the stub and and receipt from the cashier's check/money order, in case it is lost or they claim they didn't get the money.

What would you do if you had the check? Probably destroy it. The goal is to render it uncashable. One way to do such is to have it shredded.
If you are uncomfortable leaving them to destroy it, then swing by and pick it up. Alternatively offer to send them a self addressed and stamped envelope. I am sure they will accommodate if you ask nicely.