After the Fund negotiates with a plaintiff or claimant a settlement offer that the Fund finds reasonable, the Fund shall give notice to the defendant or uninsured party of the offer in accordance with regulations of the Fund. If a defendant or uninsured party approves the settlement offer, the plaintiff or claimant shall proceed to settlement in accordance with regulations of the Fund and the Maryland Rules. If a defendant or uninsured party rejects a settlement offer, the Fund shall cause notice to be served on the defendant or uninsured party by any lawful manner, including: a sheriff; a private process server; and certified mail bearing a postmark from the United States Postal Service to the last known address of the defendant or uninsured party or the last address on file with the Motor Vehicle Administration of this State or the state where the defendant or uninsured was last known to reside. The notice served under this subsection shall state that: without further notice, the Fund will withdraw from the claim or action 30 days after the date of the notice; within 30 days after the date of the notice, an appearance may be entered by the defendant or uninsured party or by defense counsel whom the defendant or uninsured party chooses; and if the provisions of item (ii) of this paragraph are not met, at any time after 30 days following the date of the notice and without further notice, suit may be filed or judgment may be entered against the defendant or uninsured party in the amount of the settlement offer. After the end of the 30-day period following notice served to a defendant or uninsured party under subsection (b) of this section, the Fund may settle the claim, file suit, or request the court to set the action for an expedited hearing. At a hearing authorized under subsection (c) of this section, the court may proceed in a summary manner and, if satisfied that each applicable provision of this title has been met, enter judgment in favor of the plaintiff or Fund in the amount of the settlement offer. The defendant or uninsured party may file an appeal within 10 days after the date of entry of the judgment. Absent proof of fraud, mutual mistake, or obvious irregularity, the judgment is not subject to appeal, amendment, or other action of the court after the period for filing an appeal has expired.