I use mostly, US data centers and if there is a 'DMCA' complaint, They tell me I have 24 Hours to remove otherwise they will nullroute my IP that using the domain name.
Nullrouting is basically disabling that IP, If that domain is on the 'Shared IP' your server may appear down for common domains, but the server isn't actually off; You will still be able to access via a secondary IP; Correct the issue and the IP will be re-enabled.
Commonly, I noticed if it continues to happen they might end up fining you (never happened), terminating you (never happened) or just keep getting notices and simply respond to them.