I'm wondering because due to reasons I will not disclose, I am not allowed to make any money. I was wondering if I could give the rights to my book to my parents so I could publish it, and they could make the money instead?
If there are legal reasons you can't make money, these might also apply to transfer of assets, and rights to a book could fall under this.
[Not a lawyer], so I'm agreeing with Thomo that it would be good to get a professional opinion from one.
I have a writer's imagination, so the reasons I'm coming up with for not being able to accept money yourself are on the dramatic side, but if the reason is sufficient you might be giving your parents - or any other third party - a legal liability rather than a source of income.
Obligatory disclaimer: I am not a lawyer.
Legal rights to a copyright are just like any other property right: you can buy, sell, or trade them. Like any non-trivial business transaction, it's a good idea to have a written contract to protect everybody involved.
If this is a deal just between you and your parents, and I presume from the context you're on good terms, the contract needn't be complicated. I see others advising to get a lawyer. That wouldn't hurt, but in this case I doubt it's necessary. Lawyers cost money and it's likely the cost of a lawyer here is significant compared to the value of the asset. If you want to just give away rights, I presume you're not worried that they'll cheat you somehow. And I doubt they're worried that this is some sort of trick on your part to get them to accept money for the book and then you sue them for copyright violation. But it helps to have a written agreement just in case someone changes their mind later, or some third party gets involved, like a publisher asks for evidence that they own the rights.
If you're living in the United States, then for a contract to be valid there must be "consideration". That is, giving something away for free is not a binding contract; you have to get something in return. Even if it's something trivial. Some contracts will say "in receipt of $1 and other valuable consideration" to fulfill this condition. If you're under 18, most contracts you sign are not binding. If you're not in the US, these may or may not apply. That's the reason why people go to lawyers: because a lawyer should know what rules like this apply to you.
All that said, the obvious big question is why you are "not allowed to make money". I'm not asking you to give away personal information that you don't want to give away. But the reason might be relevant to the answer. If the reason is legal -- you're in prison in a state where prisoners aren't allowed to have outside income, or you lost a lawsuit and any earnings would have to be turned over to the winner, etc -- then it's possible that a court would suspect that such an agreement with your parents was a subterfuge, and that they were going to give you the money back under the table in violation of the law. If you're doing this to get around some legal restriction, you probably should talk to a lawyer before you land both you and your parents in prison. If it's something truly personal, like "my wife would just squander the money", then any issues it raises would presumably also be purely personal.
Contracts are not complicated in concept: two parties are making an agreement that each will do something for the other.
Think about what you are giving them. Is it all rights? Can they re-edit the book? Can they claim they wrote it? What if they sell the movie rights? Graphic-novel rights? Video-game rights?
Think about how long they keep the rights. In perpetuity? If not, what happens when the time expires?
Think about what you want in return. Is it a pure gift, or do you want to be remembered in some fashion?
Write this all up clearly as you can, print out two copies, and have everyone sign both copies.
EDIT: There seems to be a strong bias, not just here but in general, towards "letting a professional handle it". It's not an absurd position, but it's not like the obvious certainty its adherents make it out to be.
First, you have to choose the professional. You know what the guy who graduates at the bottom of his class in medical school is called? "Doctor". Just as you aren't qualified to act as a professional, you aren't really qualified to judge one. In every case, in every profession, it's a crap-shoot.
Second, you have to pay the professional. In the OP's case, what is the likely value of the rights? Well, let's be honest here: most people's literary output is worth precisely bupkis. If she were J.K.Rowling, OK, there's a lot at stake, and the lawyer's fee is well-worth it if it reduces the chance of a loss even slightly. In this case, people are recommending the OP spend $500 to protect a property not worth a tenth that.
Third, you have to trust the professional. His incentives are very different from yours. He needs to make a living, he wants to be home by six. Those goals may conflict with yours.
On April 23, 1852, lawyer Alphonso Taft, the future father of President (and Chief Justice) William Taft, filed a probate case in Hamilton, Ohio, for Ethan Stone, a wealthy man who had recently joined the Choir Invisible at the age of 83, leaving an estate of some $10,000 (about a half-million today). Apparently one paragraph, about the disposition of some land, was somewhat vague and eventually led to a lawsuit.
Which lawsuit is still going on, 165 years later.
I suspect that the late lamented Mr. Stone went to his Reward secure in the belief that his property would be distributed in accordance with his wishes.
After all, he employed professionals...