Apparently... NOTHING!
A Toronto area Toyota dealer took this 2001 Corolla on trade a couple of years ago with almost a million km on the clock, and kept it on the road as a rolling billboard.
So a reporter went out to record the odometer rolling over from 999,999 and it just... froze. No 000,000 for you!
Full story:
How a Toronto-area Corolla is driven beyond 999,999 kilometres - The Globe and Mail
How do you pack so many miles on a Corolla? In this case, it was used as a driving school car, and was religiously maintained.