Does a dead front-door light still drain electricity?

NO they don't draw any current as the filament is broken.  A LED light will last longer and use less power than either an incandescent or a fluorescent

i would say : it depends on what happened
normally if the filament is broken - there is no current draw possible, as said above
however, parts of the filament can fall down, and short the power lines, depending on lamp model, and mounting

Also depends on the exact electronics involved.

Many devices have constant low current drain.

The only way to tell for sure is to insert an AMP meter in the current path, checking if you have any current draw.

>>  Many devices have constant low current drain.  << that's why i Always put a switch in the AC line

The base is insulated from the center contact and the part that screws in. A light is one of the simplest of circuits there is.
a power source, a switch and a bulb (which is basically a resistor). There is no standby circuitry, nothing that stays on it is either ON or OFF. Off draws 0 current,

Anyway, the H.O.A requires a front-door light to be on 24/7.

Even in the daytime?  Then LED lamps would save you some cost in electricity.  How bright does it have to be?  Just put in a lower wattage LED or Compact Fluorescent and you should be able to save a lot more electricity.  (5W LED versus 40W incandescent)  If you have power fluctuations, LEDs will survive it better.  A normal LED bulb should last you a good 5-6 years in the always on position, before it fails or becomes too dim regular use.

If you are allowed to have it go off in the daytime, install a light sensor and let it turn off.  It will save you electricity and let the LED bulb last much longer.

Typical Average Rated Life for Various Types of Bulbs
Incandescent       750-2,000 hours
Fluorescent       24,000-36,000 hours
HID       10,000-24,000 hours
Compact Fluorescent
Plug-in       10,000-20,000 hours
Screw-based       8,000-10,000 hours
Halogen       2,000-4,000 hours
LED       40,000-50,000 hour

James, how about some feedback ?

I think you need to read the home owner's association "requirements" in detail before deciding what to do about the external light.  As skullnobrains has highlighted, if everybody was forced to have bulbs illuminated 24 hours a day it would be using up unnecessary electricity during the daylight hours.  Like just about every area in every developed country in the world, Delaware has had to commit to future plans with a view to reducing energy consumption and wastage, and it offers initiatives to home owners to do so.  A very quick Google search throws up pages like this:

https://www.demecinc.net/sustainability/renewable-energy-commitment/
https://www.demecinc.net/sustainability/programs-incentives/
https://www.delmarva.com/News/Pages/NewDelmarvaPowerEnergyEfficiencyProgramsApprovedbyDelawarePublicServiceCommission.aspx
http://www.dce.coop/content/energy-efficiency-programs
https://dnrec.alpha.delaware.gov/climate-coastal-energy/efficient-renewable/

I would find it hard to believe that home owners would be forced to have lights burning continuously during the day.  If they are insisting on this, they are backward in their thinking and now may be an opportune time to consult with other home owners to influnce a change of policy.

I would imagine that what they insist on is a fairly low intensity "bulkhead" light with sufficient illumination for residents to see their way along the garden path to the door and unlock it without tripping on a paving slab and fumbling with their keys in the dark.  To that end a self-contained solar powered bulkhead light is all that should be required.  I don't know how much daylight Delaware gets during Winter, but even in the dismal grey Winters in the UK there is often sufficient daylight to recharge a cheap external LED light that is fitted with a movement sensor so that it isn't burning all the time.  There usually wouldn't be enough light to charge one that stays on continuously during the night though.

Thanks all,
Sorry, I’ve been away for holiday

I double checked and the req is actually dusk til dawn.
I’m sure that changes the approach?
Light sensor?

a led light with a sensor seems to be the best solution then

Yes, an LED light with a light sensor is the way to go.  Home Depot has a filter in their outdoor lighting selection entitled "Dusk to Dawn" and you can filter it further by adding LED:
https://www.homedepot.com/b/Lighting-Outdoor-Lighting-Outdoor-Wall-Lighting/LED/Dusk-to-Dawn/N-5yc1vZc7qqZ1z0ogmrZ1z0u5o6

A ligh sensor, and a led powered with solar energy would be a good fit. You can fimd decent ones around 100 bucks, 200 tops

i would stay away from solar powered -since it needs a battere - and it's replacement everey couple of years….if it needs to burn all night

Thanks

I'll call my sister-in-law tomorrow to discuss the options, and one of my neighbors on Monday.

Hmm. I know folks using such lights for over 15 years with no other issue than wiping the captors every few years. Not sure which brand. I believe they use nimh batteries rather than lithium which would probably be today's industry choices. A bunch of capacitors would last for ever buf i am unsure any vendor would propose that.

Thanks

My bro went by there a few days ago and said all the lights were on in the community in the day! It's all good.