If I owe the IRS back taxes on a settlement that I receive from an accident case, can they keep the money for my taxes that I owe?

First of all, with regard to this "settlement" that you may receive from an accident case, I'm not sure why the IRS would enter into the picture prior to a time when you file a tax return reporting whatever might be taxable from the settlement. If this settlement from an accident is for personal injuries, those amounts are normally not considered income for the purpose of the income tax. I have a feeling, however, that you haven't explained the entire situation. Unless the proceeds are coming from the government I'm not sure how the IRS would be able to retain whatever those amounts were. If you do owe back taxes I suppose the easiest thing to do would be to pay those taxes when you receive the settlement proceeds.

Any time that you owe money to the I.R.S., they will keep any federal refund that you are due and apply it to the debt owed. Additionally, the I.R.S. may attempt to intercept any state refund that you are owed, but they must make the effort to intercept the state refund; it is not automatically applied to your federal debt, as the state and federal revenue agencies are separate from one another. Additionally, if you do not work out an installment agreement or other form of resolution for your tax debt with the I.R.S., then they may move forward with collection activities, including wage garnishments and bank levies.

Of course they are the government and therefore they make the rules and never lose the game, which is collecting money.