Say I have a website that is under DDOS attack. Assume it will be going on indefinitely. Assume my hosting provider has DDOS protection that will protect my servers but at the same time users will be unable to access the website.
How can I survive being targeted like this? Cycling IP addresses and updating DNS ad infinitum does not seem like viable solution... because in the end, it's the network attacks that get you, not the application level attacks.
What is your business? How much traffic "normal" do you get? What is the size of the attack? What is the bandwidth of your upstream connection? Who are your customers? Where is it hosted? What are your acceptable thresholds for false negatives and positives? Do you know who is attacking you and why?
Most every hosting provider will have some sort of DDoS monitoring and mitigation on their networks already. Their response to sustained or repeated attacks might range from scrubbing the bad traffic before it gets to you and not notifying you at all, to reaching out to you to work with you on both ends of the issue, to cancelling your account.
If you just have a fairly simple website that you host yourself, Cloudflare likely a fine option. If you have more advanced needs, you should talk to a more comprehensive DDoS solution vendor.