Here's my best guess. They will have a supply of disposable masks at the ticket counter. If someone shows up without a mask, they will hand one over.
If they run out, then the passenger will not get a boarding pass and will be asked to procure their own mask somehow. I can imagine enterprising home-sewers setting up sidewalk vending for masks, so that passenger can go outside, get a mask, then come back.
Personally, I plan, once I can start flying again, to get four or five homemade cloth masks and take them with me in my carry-on. That way I can switch to a new, fresh mask when I feel it necessary and won't have to rely on the airline-supplied masks. Once at my destination, I can wash out the dirty masks, hang them up to dry overnight and then go on my business.
Where I live, there are plenty of under- and un-employed people making a few bucks selling masks. I have no problems buying masks from them thus helping keep their families afloat.