Well, Here's what will happen in order. The Original Copyright owner will send the DMCA report to Cloudflare. Cloudflare will forward that report to you and your Datacenter ( hosting/server provider ) and the Provider will suspend/terminate your website.
Now, Cloudflare has your email so that they can find you. But They Don't have any details about your Hosting/Server Provider, right? Wrong, They Have the IP address of your A Record. You can find the Origin of any IP by doing a whois search.
So The Trick is, using reverse Proxy. You Have Your Regular Server IP ( Company A) and Get an IP from a DMCA-ignored Hosting (Company B) ( Mostly from the Netherlands ). And You Serve Cloudflare with the DMCA-ignored IP while your Main Server IP is being hidden from Cloudflare Too. This way, when they send the DMCA takedown notice to your DMCA-ignored IP provider (Company B), They Just Ignore it and You will too. And Company A will Do Nothing because they will never get the Take Down Notice.
Just Don't Play with anything Gov Related and Your Website Will Live as long as you wish.