We split the dose but if we were using one injection a day and forgot to take it in the evening then I'd split what you usually do in half and give that half in the morning and then inject as usual that evening. I'd then keep an eye on your readings through the day as you may need some fast acting correction injections if you're running too high or extra snacks if you're running a bit low. Not ideal but that's how I'd handle it.
I too agree with Sophie, inject half the amount the following morning and if need be include a correction dose of QA insulin with your morning breakfast dose. Were you to inject the full dose of background insulin the morning after you forget it would overlap with your usual evening dose and may send you hypo in the early hours the following day.
I do use 1 dose background a day and did forget a few months back. I did reduce the dose in the morning, had to have slightly higher breakfast dose to bring in to line but otherwise was fine