Unclaimed publications may be disposed of in accordance with the Federal Depository Library Handbook pp.5-21 - 5-24, once the Regional notifies the library that the Offers list has been taken down. The Handbook directs selective libraries to make a "reasonable effort" to place withdrawn publications in public, school, or other non depository libraries in their area.
All publications weeded from the depository collection should be clearly marked as "withdrawn" by the offering library prior to any disposition. This will help prevent future misunderstandings. Tearing off the covers also helps identify documents which are to be discarded.
Recycling is perfectably acceptable, and encouraged, as a way of disposing of depository materials.
National N&O & Pre-1907 Materials
Virginia depository libraries should consider posting offers to the National Needs and Offers List after posting on the state Offers List. The ASERL Disposition Guidelines (pp.11-12) recommend that libraries pay special attention to documents earlier than 1907, and strongly consider offering these on the National N&O List. There were many fewer depository libraries prior to 1907 and those materials may be rarer than newer titles.