Yes, there are housing programs and policies in place that help homeless persons and persons living in a shelter receive housing assistance.
Some housing authorities participate in the HUD Homelessness Prevention and Rapid Re-Housing Program, which assists persons who would be homeless without help from this program. Please visit HUD's HPRP website for more information.
Also, many waiting lists have preferences that place qualified applicants higher on the waiting list than general applicants. Persons living in a shelter and homeless persons is a preference that may be found on an application. The specific qualifications vary depending on the housing authority or apartment community offering this preference. More information about preferences can be found here.