I am in the middle of this right now.
What happens with IRAs or 401k accounts is that they are "equalized" for the years of the marriage. So the amounts contributed/earned during the marriage in both parties accounts are balanced against each other, and the one with the lower amount is given an amount from the higher account (i.e. my STBX has an IRA worth about $13000, and I have a 401k from work that is worth considerably more; I also have an amount in the account that was earned prior to our marriage; his IRA and the pre marriage amounts are deducted from the balance in my account, and he should be awarded 1/2 of the balance).
Now, if the retirement account funds are transferred via a QDRO (qualified domestic relations order) the receiving party has the right to do whatever they want with the funds. If the receiving party decides to cash out the balance, the 10% early withdrawal penalty is waived. This was put in place to assist a spouse who has no source of income and has no retirement account from being forced to defer funds until retirement if they did not have enough money to survive. So if Minnie Me's xH decided to cash out the balance of his account, he WOULD pay the 10% early withdrawal penalty. She would not, since it is being awarded to her. However, she would be subject to normal income tax on the money.
However, I would also advise her, as others have, to roll the funds into an IRA for her and her daughter down the road. I think it's important to look at the larger picture and see the long road. I also, given the information she's provided, don't feel badly for her xH if he has gotten himself into a financial predicament. At this point it is not up to her to get him out of trouble. She needs to be thinking of herself and her daughter at this point.
As for those who feel that if he dumped her, he should suffer, I think that every situation must stand on its own merits. If he walked out on her and her daughter for the "office floozy" then I also would tell her to have no sympathy for him. If their marriage fell apart on its own, without outside influence, then it's a different story. Here in NJ, it doesn't matter why a marriage fell apart, it has no bearing on settlements.
Each situation is unique and stands on its own. I know that in my case, there was no infidelity and no other party involved. There were years of disappointment and avoidance of the issues, unemployment and refusal to take any responsibility for his part in the demise of our marriage. I have 2 children who I did not want to grow up thinking that treating a wife with disrespect is normal in a marriage. I wanted more for them, so I told him I wanted a divorce. Unfortunately, because he was willing to stay in a bad marriage, being miserable for the next however many years, he spent a year refusing to more towards settlement and it's been a horrible year for everyone. Because I have been in a stable career/job for almost 18 years, I will be the one whose 401k will be diminished, even though I managed to fund it through years of him only contributing unemployment and my paying off 5 figures of debt that we had accumulated over the years. Now we are debt free (except for the cars and house) and I will be able to stay in our home and carry it on my own.
Many men are "victims" and managed to portray themselves as being unable to manage and needing help. I took care of everything for all the years of our marriage, partly because he could not and partly because he wanted no part of knowing how bad things were financially. Now, he resents all that I did, claiming I "controlled" everything. Well, frankly, someone had to LOL!
OP, only you can decide what you want to do with this money. But my advice, from someone who is about to lose a good chunk of her 401k funds, would be to roll it over into an IRA for your future. Let your xh manage his own finances now.
I wish you much luck in the future.