If your trustee determines that there's no sense in selling an asset, he must give notice of his decision to you, the court and your creditors. Your creditors have a right to object if they think the asset does have some value. For example, a creditor might believe that your home will sell for more than the mortgage against it. After satisfying the mortgage, there might be some proceeds left over. Creditors can file a motion with the bankruptcy court within 15 days to try to stop the abandonment and force the trustee to sell the asset. A judge would ultimately decide whether the trustee can abandon the property.
If your trustee abandons an asset, you still own it. If there's no loan against it, it's yours to do with as you like. However, if there is a loan against the property, your bankruptcy proceedings don't affect this lien. The abandoned property and its loan fall outside your bankruptcy, so the lien is not dischargeable and you still owe that particular creditor. You may get to keep the asset, but you won't get out from under any payments you owe on it.
After your trustee abandons an asset, and if there's a loan against the property, the creditor will probably ask you to "reaffirm" it. If you agree, you'll enter into a new contract with the creditor, agreeing to continue paying the debt associated with the asset. If the asset is your automobile and you decline to reaffirm the loan, the lender will repossess the auto. If the asset is your home and you don't reaffirm, the mortgage company can begin a foreclosure action. If you're keeping your mortgage payments current, however, there's a possibility that the company won't foreclose even if you don't reaffirm.
Occasionally, a trustee might intend to abandon an asset, but forget to issue notice to your creditors. As long as you listed the asset in your bankruptcy petition, abandonment is automatic when your bankruptcy is final and the court has discharged your debts. The trustee can't reopen your case to claim your asset and sell it after your bankruptcy is over. If you're not comfortable with this and your bankruptcy is still pending, you can file a motion with the bankruptcy court and ask a judge to order the trustee to issue the notice. The downside to this is that you can't be sure if the trustee has simply forgotten to issue the notice, or if he hasn't made up his mind yet whether to abandon the property. If the latter is the case, your motion could prompt him to sell your asset instead.
Reversal of Abandonment
Your trustee can reverse his decision to abandon an asset, even after giving notice. However, this typically only occurs if you lied in your petition about something that would affect the asset's value.