Short answer: you unleash a hellstorm of court proceedings.
Long answer: If you don’t turn over your tax refund monies after the trustee demands them, then various bad things can happen to you. In a chapter 13, you are required to turn over your refunds for the next three years. If you fail to do so, the trustee will dismiss your case. Sometimes, the trustee will dismiss your case and request that the court bar you from filing a new case for 180 days. This means that you can’t go bankrupt, can’t stop garnishment, and can’t avoid creditors for 6 months from the date that it is dismissed.
In a Chapter 7, it’s even worse. If you don’t turn over your tax refund, the trustee can and will file a Motion for Turnover (requiring you to turn over the refund). If you still don’t comply, then the trustee will file a Motion to Revoke Discharge, and your chapter 7 bankruptcy gets thrown out, you still owe the trustee the tax refund money plus his/her legal fees, and you can never get a discharge of those debts in a new Chapter 7.
This is why I warn my clients about losing their tax refunds and remind them that it’s worth it in the short term to get rid of a lot of debt.