Often, yes—an inherited Delaware house can be sold before the estate is finished once the right person has authority to sign. The Register of Wills issues letters testamentary when there is a will and letters of administration when there is not. A personal representative needs those letters to act for the estate, but the letters do not automatically give the representative a right to possess the house; the house must also be listed in the estate inventory.
Check whether the will gives the personal representative power to sell. If it does not, the representative may ask the Court of Chancery to approve a sale when the estate’s money and other personal property cannot pay its debts. If neither path applies, the people who inherited the house usually sign the deed together. Start with the will, letters, estate inventory, and any court order; the closing attorney or title company can confirm who needs to sign.