Nah, the good webhosters use containers for there shared hosting... if a website get's hacked other websites on the shared server won't get attacked, because the hacker is stuck in the container. (Gen4)
Containers aren't primarily used as a form of protection when a website on the server gets hacked. Proper security measures put in place however will. Containers (cloudlinux, betterlinux) are primarily focused on server density and the ability to put up to 5 times more customers on to each server. So, in words that most would understand, the capability to oversell a server where any reliable and responsible hosting provider would never do so. Using proper software configurations each website/application will be isolated from the rest of any said customers accounts (open_basedir protection, mod_userdir protection, etc). I personally wouldn't recommend any hosting provider that utilizes technologies such as Betterlinux & Cloudlinux as due to the extreme capacity load they put their servers under, they need to reduce your accounts capabilities to justify (i.e. inode restrictions, very low PHP memory limits, etc). Most websites that are hacked these days fall under two categories.
1. Wordpress users who fail to maintain their websites.
2. Customers who fail to use secure passwords on their websites/emails.
When a cPanel account is gained access to, the attacker only has access to whatever is within the said account (i.e. they can't gain access to another customers cpanel through someone else's cpanel). When one website is hacked on a server, that does not mean that the others are vulnerable as well, in fact these attacks are usually targeted to one account and that account only.
If you believe otherwise, someone has been filling your head with nonesense in attempt to sell you their service/product. 99.999999999% of security that needs to be worried about is the customer's website platform and how they store their passwords. The other 0.999999991% would be that of the host's responsibility.
With a DOS attack, all websites on that server will be unavailable.
This statement is true and false. Any reliable hosting provider will have DDoS Protection methods in place. As an example my customers are protected for attacks upwards to 160Gbps without seeing any latency/outage. So, say one customer on my server was getting hit with a 2Gbps DDoS Attack (larger than average size), nobody would notice this, not even the customer that is being attacked. Reason being the traffic coming into the datacenter gets cleaned before it makes its way to the servers that I put my customers on. Looking at traditional budget hosts over, those $1 hosting providers that everyone seems to think are so great, they do not provide features like this. As a result, if one user gets attacked on the IP that you are utilizing, rather than filtering the attack using state of the art hardware they null-route the IP for a few hours until the attack is over, knocking everyone's service out.
This is why I always recommend that people stay away from those $1 budget hosting providers, or any EIG brand provider as a matter of fact.