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Those who are VAC-Banned cannot enter a VAC-enabled server. However, this only applies to the engine the game uses. For example, users that are banned on Counter-Strike or Half-Life, will be banned on all games running the GoldSource engine. However, they can still play games and connect to secure servers on games that do not use the same engine. VAC banned players are still able to play on all VAC-insecure servers on any game that the ban had an effect on.
In the past, those who were VAC Banned had all non-purchased items deleted from their backpack. In the current version of Team Fortress 2, users who are VAC banned do not lose any items in their backpack. Instead, all items they have are stuck inside of their backpack and cannot be traded away, placed on the Steam Community Market, or transferred to other accounts in any way. This is done to prevent players trading the items to another account and cheating again. These users are still able to purchase items off of the Mann Co. Store, and use said items freely.
VAC has several versions. For example, Team Fortress 2 uses version NN. VAC is module based, and most clients only see a fraction of all the modules the system has. If the system is blocked in any way or if there is a hardware problem on the user's computer, then the user will not be able to join VAC Secured servers until said problem is fixed.
VAC bans are non-negotiable. With a few exceptions due to false positives being triggered by specific known software or hardware incompatibilities, no VAC bans are removed.
VAC targets cheats that tamper with game code and memory on the client. Cheats done by the server or involving altered data files are not subject to VAC enforcement.
As with any anti-cheat, it is not perfect. Certain cheats may be able to slip through the cracks, if only for a while. Once VAC has detected a user cheating, it may take from a few days up to a few months before said user is banned from secure servers. This is done to prevent being able to pinpoint the exact cause of the ban. Additionally, VAC runs differently on Linux machines, making it much less effective and easily bypassed. Valve has not talked about any fix for this as of yet, but in a recent Q&A with Valve CEO Gabe Newell, he has said that Valve Anti-Cheat is one of the things that they will be working on improving in the future.