NEW YORK — Borders Group, the nation’s second largest book store chain that once operated over 1,000 stores, appears headed for liquidation after a judge on Thursday approved its motion to auction itself off with a team of liquidators as its opening bid.

The move came after an offer made earlier this month from a private-equity investor disintegrated overnight. Borders said it will accept bids until 5 p.m. Sunday and will give notice by Monday if no other bidder emerges.

Earlier this month private-equity investor from Phoenix offered $215 million for the company, plus the assumption of $220 million in debt.

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