With the standard set-up, members can only book onto an event up until the day of the event. However, if you have members that turn up on the day, and you want them to book and pay for it after the event has happened, you can do this by adjusting the Sell To date.
In the administration panel, find the event and click on edit. Scroll down to the date section for the event, and click on the Selling Dates link. You may also need to View Past link if you can't see the event date that you are looking for.
Add a Sell To date, which is in the future. This will re-open the event for bookings, and allow late members to book and pay for tickets to the event.