I recently had a guest ask for a late checkout lasting until after they returned from their job site that day to pack and take showers, and I granted it saying "no rush". However, it turned out that the local job that they were working on went past 10PM and they then said that they could be out by midnight.
Since they had been there 10 nights already and paid for that, and no one was checking in the next day, I still thought that I would cut them some slack and not charge for an extra night or fee at that point. But it turned out that they did not leave till 5AM the next morning. At this point I was compelled to charge for the extra night. (As a side note, I have an outside security camara and can see people coming an going from my cell phone or PC..... I advise all my guests of this fact just to give full disclosure).
They were perfectly willing to pay for the extra night and apologetic (really nice and considerate hard-working guys) but there is no way in the Airbnb system to revise the reservation "after the fact", either by me or them. The host can find it in the "past reservations" listing but cannot revise it in any way once the check-out date has passed.
That just leaves the Resolution Center where either a guest can Send extra money or the host can Request extra money. You can dig around in the site for this or simply go to https://airbnb.com/resolutions (USA site I believe). If not already logged in, you will need to log in and it will take you to the appropriate screen. There is no choice for requesting the extra night, so I chose Other, entered the calculated amount for the extra night (since they were there for over a week I included my weekly discount. I typed a note to the guest restating the reason for the request and thanked him. I think that airbnb probably does not collect our local occupancy tax or perhaps not even the service fees in these resolution cases, but I dont know for sure yet).
I expect that all will go smoothly, and it is all documented within the messaging system. But according to Airbnb guidance, I will contact Airbnb if not resolved within 72hrs. My lesson is that I need to give a Specific late checkout time and advise that early on that I will need to charge for an extra night (or partial fee if that is even possible) if it goes past that, and allow for enough time to be able to revise the reservation in the system (although I am not sure if the host can revise it but instead the guest needs to requrst it and the Host accept it). But even if that is not possible, I think the Resolution Center is a fairly good solution, and documenting everything via the messaging system is important. I'll repost here if not resolved in this particular experience.