ZDC Center Controller reported having to manage an aircraft's landing at RIC without a direct line to RIC Tower after being informed that an area of PCT TRACON was ATC-Zero due to staffing issues.

Narrative

Aircraft X landing RIC during the night shift transitioning to Approach from the south. Aircraft asked about braking action so I called James River area of Potomac Approach. After the third unanswered call; someone from a different area there picked up and informed me that the James River area was ATC-0 and that Center (me) was expected to transition the aircraft to Tower. No one had informed ZDC Area 2 that James River was ATC-0.Since I had no direct line to RIC Tower; I found a dial number in the SOP and called. They informed me that Runway 34 was the only runway being plowed and that they'd have an operations vehicle do a braking action check; but that they had no way of getting ahold of me directly. I informed them that I would call back in 10 minutes with an arrival estimate and for a braking action report.The aircraft informed me that they would have to do the ILS 34. I pulled up the approach plate and noted that the approach started at JUVPO intersection; 8.9 miles from the threshold and that the crossing altitude was 1700 with no procedure turn available. I also noted that the Minimum IFR Altitude (MIA) in that area was 2400. I informed the pilot that he would have to cross that point 700 feet high and the pilot took a minute before informing me that they would attempt the procedure as I described. I gave the pilot alternate contact instructions in case of a missed approach and then switched them to Tower.I called Tower again to inform them of the aircraft position and approach being used. Once I lost the aircraft on radar at about 200 feet; I waited about 2 minutes and called the Tower back to verify the aircraft had landed.Also of note: During this time; several areas at ZDC were at ATC-0 due to no staffing because the headquarters refused to use their easiest remedy and pay a couple of controllers to be ready on crew rest (as we had been doing for decades during inclement weather). The Mount Vernon area of Potomac was also ATC-0.It is criminally negligent that we don't have a viable contingency plan for a sector/area closure due to staffing/emergency. It is criminally negligent that an entire area of a facility closed and no one informed the primary overlying Center sectors. It is criminally negligent that I asked; almost a year ago; to have extended runway centerlines for RDU; RIC; and ORF depicted on a map toggle on our scopes. We had a similar issue on multiple nights with RDU where I asked for this repeatedly.If there is any chance of us taking over an Approach Control's airspace; there should be a direct line to and from the Tower to the Center sector. How were they supposed to release departures or tell me about ATIS changes? I guess they can call the front desk and hope the Operations Manager in Charge (OMIC) isn't busy?We should in no way be responsible for an approach procedure where the aircraft can not safely intercept the glideslope due to our altitude restrictions… again. This would be mitigated with displayed extended centerlines. All controllers should be trained annually (actually training off the floor) on the ATC-0 contingency plans for all adjacent airspace. I'd be more than happy to sit in a room with upper management and the running" things from a desk at headquarters to discuss any of this."