Yes, yes he can.
That being said, I’m an attorney, and every answer has a bunch of caveats (disclaimers).
Children under 18 —
Car. If your child is under the age of 18, you own everything that is “his.” So if you buy a car for your son and give it to him for Christmas, if he’s under 18, you have to be on the title. If you are on the title, then it’s yours.
Cash and Bank accounts. When you set up a special bank account that is for your 6 year old daughter, the bank will require you to be on the account, because she is a minor. So let’s say you give her $500 for Christmas and deposit it into her account. In your mind, it’s her money, and she can use it for whatever she wants. She’s 6! it’s your money.
Electronics. My 6 year old desperately wants a $50 drone for Christmas. I know this will end up badly, but I’m going to get it for him. The bk trustee won’t care about a $50 drone. On the other hand, if you buy your 14 year old a $1,000 iphone, that’s a problem. She’s under 18, so the phone is yours, and the bk trustee may be interested in it.
Children over 18 —
You have to be very careful with giving gifts of substantial value to anyone before you file bankruptcy. In an extreme example, I’ve had a client who “gifted” her $15,000 truck to her brother one month before filing bankruptcy. She didn’t tell me about it. At the 341 Meeting of Creditors, her Chapter 7 Trustee definitely had some questions!
For a more realistic example, the bk trustee can scrutinize anything you give away before filing bankruptcy. This may be the year to give a card with a heartfelt poem, or even some of those personalized socks with your face on them. If you give $500 to each of your 4 children, that’s $2,000 that you gave away before filing bk. There is a good chance that the bk trustee will want to get that money back to pay your creditors.
Presents from someone else (like Grandma and Grandpa) If your child is under 18, that is your property. There is still a chance that the bk trustee will take it.
It sounds awful, but it’s the bk trustee’s job to review your assets (including gifts and transfers) to see if there is anything she can use to liquidate and pay off your creditors. If you have a question, you should ask your attorney before you make the transfer.