I've been reading about oxygen therapy, and at first was a bit surprised how inefficient it is. The actual human use of oxygen at rest (the amount that gets used as an oxidizer and ends up as CO2 or water) is about 0.25 liters per minute, yet oxygen concentrators meant to adequately supply a single person normally put out about 5 liters per minute. And although the oxygen concentration coming out of the machine is 90% or so, inefficiencies in the way it is actually delivered to the mouth and nose reduce that to where patients are usually breathing a concentration of less than 50% oxygen (as compared to the normal 20% oxygen concentration of the atmosphere).
Oxygen is cheap, so most of the time this inefficiency doesn't really matter. Nor does the low delivered concentration: pure oxygen can be toxic and is usually unnecessary. But this does mean that if necessary to handle the coronavirus pandemic, we could stretch oxygen supplies a long way and/or increase the delivered concentration.
Part of the reason for the inefficiency is that the breathing rate is about 5-8 liters/minute for a resting person. So the output of a 5 liter/minute oxygen concentrator is somewhat less than that, to start. And about half the time the person is breathing out, so in simple setups the oxygen delivered during that time gets blown away and wasted. Some oxygen masks have a bag to store oxygen momentarily and valves to let that oxygen in and redirect used air out. In other setups, sensors are used to detect when the patient is exhaling and shut off oxygen. But though some setups are better than others, the usual numbers given for the delivered oxygen concentration are nowhere near 100%. And they all waste exhaled air: even when the body has only lowered the oxygen concentration in it from (say) 40% to 35%, the exhalations are just let out into the room. Although that air has a lot of oxygen in it, it can't simply be reused, since it has carbon dioxide in it; carbon dioxide buildup is first uncomfortable and then toxic.
But there is a technology that uses much less oxygen. The Navy SEALs use it: rebreathers. These have scrubbers which strip out the carbon dioxide, so that the exhaled air can be reused. Oxygen is only added to it in the amounts that the body actually uses. Militarily, this means not only using much less oxygen but not giving away your position with a stream of bubbles. Scrubbers suitable for underwater duty can be a bit complicated, but ones for hospital use could easily be improvised: bubble the air through a solution of sodium hydroxide (lye), which is cheap and easily obtainable. Some filtering of the output air might be necessary to remove tiny particles of lye put into the air by the bubbling process, but that could probably just be done by bubbling it through a second jar containing pure water. The power for the bubbling could either be provided by the patient's own breathing (through one-way valves) or a small air pump.