It did, a new company - also called Alitalia was founded to continue operations.
Following excerpt from
Wikipedia regarding what happened
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In August 2008 Alitalia went bankrupt. Compagnia Aerea Italiana (CAI) bought the Alitalia brand and some assets for 1.052 billion ($1.33 billion), paying 427 million in cash and taking on 625 million in Alitalia debts on December 12, 2008.
On 26 August 2008 a group of Italian entrepreneurs along with Intesa Sanpaolo, one of the major Italian banks, founded Compagnia Aerea Italiana (CAI) with the aim of buying the trademark and some of the assets of the bankrupt Alitalia Linee Aeree Italiane and to merge these with Air One, another Italian carrier. Only the Alitalia trademark would be kept for the merged company.
On 30 October 2008 CAI offered 1,100 million to acquire parts of the bankrupt airline. The offer was submitted to Alitalia's bankruptcy administrator despite refusal by some pilots and flight attendants' unions to agree to the rescue plan.
The bankruptcy administrator and the Italian government, major shareholder of Alitalia, agreed to CAI's offer on 19 November 2008. Alitalia's profitable assets were transferred to CAI on 12 December 2008 after CAI paid 1.052 billion ($1.33 billion), consisting of 427 million in cash and the assumption of responsibility for 625 million in Alitalia debt.
On 13 January 2009 the new Alitalia re-launched operations. The owners of Compagnia Aerea Italiana sold 25% of the company's shares to Air France-KLM for 322 million. Air France-KLM also obtained an option, subject to certain conditions, to purchase additional shares after 2013. The French as well as the Italian boards agreed to the sale.
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