1. If you have a scheduled book signing event at a Borders store, it may or may not happen. Borders plans to close 200 stores over the next several weeks. They have not yet indicated which stores will close. You'll just need to wait and see if the store hosting your event is affected.
2. It may take longer for you to get paid for any books you have sold through Borders. Borders has been delaying payments to some publishers and distributors. Some publishers have stopped shipping product to Borders altogether.
3. You won't be able to schedule any additional book signing events at Borders. At least for now. Borders has instituted an ordering freeze on additional books. Also, Ingram, a major wholesaler and distributor in the U.S., has stopped shipping books to Borders. If you want to schedule a book signing event at a major bookstore chain, it likely won't be at a Borders store for the foreseeable future.
Borders says its business operations will continue as usual, but as you can see, from an author's standpoint, some things will definitely change. If you are a fan of Borders and would like to see them continue operating as a national bookstore chain, the best thing you can do is visit a Borders store or Borders.com and make a purchase.
This is one more example of why authors can't totally rely on bookstores to sell all of their books. Customer buying habits are changing, and authors need to hit the niche market for their book to effectively reach their readers.
UPDATE: Borders has now released a list of the stores they will be closing.