Veteran Deportation Prevention and Reform Act This bill limits the deportation of noncitizen veterans and addresses related issues. No federal agency may initiate removal proceedings without asking the individual facing removal whether the individual is a member of the Armed Forces, a veteran, or a spouse, parent, or minor child of such an individual. If an individual responds in the affirmative, that individual may not be removed until (1) the relevant Department of Homeland Security (DHS) agency has transferred that individual's case files to an advisory committee created under this bill, and (2) that committee has provided recommendations as to the outcome of the case. DHS must create a system to share information across various agencies about noncitizen veterans who may be subject to removal to ensure that such a veteran's military service is taken into consideration in immigration-related cases. DHS shall also create a system for (1) identifying noncitizens who are or may be veterans, and (2) collecting data relating to such noncitizens who are in removal proceedings or may have been removed. DHS and the Department of Defense must jointly carry out a program to naturalize a noncitizen (and certain family members) if the noncitizen serves on active duty in the Armed Forces and is not otherwise ineligible for citizenship if that noncitizen submits an application. DHS must also establish a program for eligible noncitizen veterans (generally those not convicted for certain serious crimes) to obtain permanent resident status. Similarly, the Department of Justice must provide permanent resident status to such eligible veterans in removal proceedings.