If you do not get placed on at waiting list, it depends on the housing agency's policy if the copies of your personal documents (such as your photo ID and Social Security Card) will be returned to you.
A lot of housing agencies do return these documents, but it is not a guarantee. If they are not returned, they are likely stored securely or destroyed. However, if you contact the housing agency and request these documents to be returned, it's likely the documents will be returned.
Contact the housing agency you applied to for more information. You can use the search bar on the top of this page to search for housing authority and apartment community contact information.