Yes, but not immediately. An expired domain goes through a recovery period first, during which only you can renew it. Once that period ends and the domain is released, anyone can register it, and expired domains with any history are picked up automatically within minutes.
What happens in between
Most extensions run roughly the same sequence: a grace period at the ordinary renewal price, then a redemption period at a much higher fee, then a short queue before release. The lengths vary far more than people expect, and they are set by the registrar as well as the registry.
Throughout all of it the domain is not resolving. Your website and your email are both down for the entire recovery window, because both depend on the same records.
Who takes them
Not people browsing for names. Automated services monitor the release queue and register anything with traffic, inbound links or an established history the moment it becomes available. A domain a business has traded on for a decade is exactly the profile they look for.
What to do if yours has expired
Act the same day. Log in to your registrar and renew, even if the panel shows the domain as still active — that display can lag behind what the rest of the internet sees. If renewal is no longer offered, ask support about redemption before assuming it is gone.
This is the short version. The full guide covers it properly: read more.