every single website will go through the same process when it expires, no matter what rankings it has.
Once the due date arrives and website owner does not pay, the domain is parked for a couple of days to give the owner time to renew without additional costs.

When that grace period ends, the owner is still able to renew it but usually with some kind of penalty fee.

After that, the ownership of the website is forfeited or lost and that domain is now considered an expiring domain. The domain is auctioned and sold to the highest bidder during this stage.

If no one buys or places any bids, I believe it is now considered an expired domain where anybody can pick it up after paying a fixed price (no more bidding).