There is going to be a difference here between a ticket which includes an visa free airside transit and a ticket which gives you an onward leg separate to your existing ticket, even with the same airline (but especially with a different airline).

@Moo Thanks, sorry what do you mean by "visa-free airside transit"? A layover without going through immigration and without requiring any visa?

Yup, but that might not exactly fit your question after a second read.

I've read numerous posts here over the years from people who have done exactly this.

@MichaelHampton thanks, just to confirm, they purchase it at the last minute / after being refused check-in/entry and they had no issue afterward to get to the plane?

Yup, if it’s just a “you need an onward ticket”, then buying an onward ticket satisfies that requirement and you can carry on checking in.

@Moo so if the airline or immigration officer rejects the traveler due to lack of onward ticket, the traveler can simply ask them to wait for two minutes, buy a ticket on their phone and then the airline/immigration will be ok¿

@FranckDernoncourt it satisfies the requirement, so...

@Moo I'm not familiar with all the details, if any, around the onward ticket requirements.

In many cases, I'd expect this would be at the immigation agent's discretion. They could allow you a few minutes to buy the ticket, or they could immediately stamp your passport "rejected" and order your removal without giving you the chance. I hardly think there will be a general answer that covers every country on the globe.

Depending on the country, the immigration officer may be a different case from the airline. Some IOs make a judgement call on whether someone is a genuine visitor taking into account all circumstances, and might consider the need to purchase a ticket as indicating lack of real intent to leave on time. Also, the area where this happens is often a no-cell-phone zone, making ticket buying difficult.

@NateEldredge thanks, is there a way to get some probability of this happening ahead of time?

I can't imagine how one would measure or estimate that probability. Given the rarity of this situation, it seems unlikely there is enough data.

@NateEldredge if it rare I guess it means low probability :)

@FranckDernoncourt Getting to the point of being in front of an immigration officer without a required document is rare, because airlines try very hard to make sure all passengers have the right documents. Because of that rarity, it is difficult to know the ratio of immediate denial vs. being allowed to use a phone to buy a ticket on the fly.

@PatriciaShanahan oh I see, got it, thanks! How do we know if onward ticket is required (i.e., is among the set of "right documents")?

Timatic has a special phrase for it: "Visitors not holding return/onward tickets could be refused entry."

There's also an explanation: "Immigration authorities may request visitors and transit passengers to prove that they will depart from the country within the prescribed period, by showing a return or onward ticket to their next international destination. Unless stated otherwise, return/onward ticket is defined as: a. International airline ticket (i.e. any types of airline tickets, reservation confirmation, booking code etc.); or

b. Evidence of departing from the country by other means of transportation (e.g. confirmation of joining a cruise, train, bus or ferry tickets, proof of departing by private boat or plane, etc)."

@Franck Dernoncourt It might help get an answer from those who’ve been in this situation if you specified the country(ies) you’re particularly interested in. For example, I’ve checked in several times for a flight to Cuba (a destination for which the ‘May be refused entry’ warning appears in Timatic) with a separately-booked return ticket; I’ve never been asked for evidence of my return flight at the outbound checkin desk, nor have I been asked for it on arrival in Cuba or when extending my 30 day tourist visa there.