Filing for bankruptcy does not automatically mean that a company will go out of business. Many companies have filled for bankruptcy yet came back to be extremely successful. It all obviously depends on whether they file for liquidation or restructuring.
Borders should be fine...hopefully. Close some stores and focus on profitable markets. Honestly, I prefer the wider selection at B&N. However, If prefer buying my magazines at Borders. Borders also has better "sales" and coupons than B&N. Though, that may be partly why they are losing money. If I buy a new book from a physical store, it's usually at Borders.
Though, I've been buying mostly used books...online but also at Half Price Books (which is an awesome chain). I also use Amazon too much since their low prices and lack of tax makes it difficult to resist.