Many repositories can devote a limited amount of time to answering such requests, depending on the nature of the inquiry. Some special collections make use of off-site storage. Retrieval of off-site materials requires advance notice. Check with each individual collection about its procedures. In order to best ensure access, call ahead and discuss your needs.
Permission is required to duplicate materials in special collections.
Since policies vary, researchers should discuss their needs directly with the staff of the appropriate repository. At times, microfilming will be required as an alternative to photocopying. The staff will discuss with the researcher the process involved and the costs the researcher will incur. I'm interested in donating materials to a special collection at Yale. You should get in touch with the librarian or curator who is responsible for selecting materials in the appropriate subject area.