Is there any way I can receive priority placement on a waiting list?
Yes. These criteria are referred to by HUD and Public Housing Authorities as preferences.
There are many preferences that are permitted and employed in both Public Housing and Housing Choice Voucher waiting list management.
Common preferences include local residency (applicants who reside in or have full time employment in the jurisdiction of the housing authority), persons with disabilities, seniors, veterans, homeless persons, victims of domestic violence, working families, victims of natural disaster/government action and families with children. There may also be other preferences for a waiting list not identified above.
The two most common (usually of equal weight) preferences are for seniors and persons with disabilities. The third most common preference is local residency.
The local residency preference is an interesting one. It is illegal for housing authorities to restrict eligibility based on a potential clients current location, save for a very rare circumstance that must be approved by HUD. Generally, if a resident of Washington DC wants to apply to a housing waiting list in northern Virginia, they may do so. However, if that PHA in Northern Virginia wishes to prioritize serving current residents over "out of towners," they may establish a local residency preference.
Any new applicants to the waiting list are ranked according to their preferences. Usually, points are allocated to various preferences and applicants are ranked by points. It is possible and common, for applicants to have more than one preference, ranking them even higher. The effect of this is usually anyone without a preference sits at the bottom of the list and never gets served since the programs are already oversubscribed.
A PHA's preferences must be in accordance with the federal regulations for each program and be published in the PHA's annual and administrative plans.