I have exactly this situation. One person booked but at least two used my property.
They now argue it was an AirBnB sopftware glitch which prevented them from entering two persons at the booking stage. So actually now saying: "Yes I know we were underbooking". Nobody else seems to have had these problems with the booking machine so rather unlikely. I will certainly not be getting into any sort of argument with the people involved who now also argue that they used the word "we" in their correspondence with us. So it is our fault?
I believe this issue with "underbooking" is now common practice with AirBNB because so many hosts are not on the premises to check either on arrival or departure.
I am leaving it up to AirBNB to sort the issue out.
At the moment I have somebody who looks after my property while I am away and I will be returning in the next few days. Until then I have decided to block the property on AirBNB's system. I will however allow bookings from Booking.com where I believe this is not such a common problem because the hosts on booking.com are often boardig houses and small businesses where it is much more likely that somebody will be at the property to hand over the keys when the guests arrive.
It might be wise to indicate in your description that guests will be met on arrival even if you are not actually always going to be there.
IWe actually have a second property in Germany where the situation is quite different in such cases and I have had personal experience where somebody was arrested. The rules in the BRD (I only have them in the original German Version) are:
"Ist einem zukünftigen Mieter bereits bei Unterzeichnung eines Mietvertrages bewusst, dass er der Verpflichtung zur Mietzahlung nicht nachkommen will und/oder kann, begeht er mit dem Vertragsabschluss Einmietbetrug. Er täuscht den Vermieter also vorsätzlich mit falschen Tatsachen bezüglich seiner finanziellen Situation – und macht sich damit strafbar. Vermieter können deshalb zivil- und strafrechtlich gegen den nicht zahlenden Mieter vorgehen."
As one can see this is a specific crime and can be followed up both by prosecution and civil litigation. Let us just hope that enoufgh people get caught out and it becomes public enougfh that potential swindlers will think twice about putting too few people in their bookings.