When banned on steam, I believe you are still about to download and play your (offline) games.
My understanding is that your account is effectively made read-only (blocked from purchasing, community, etc) and not removed entirely. Steam's help article on restricted accounts[1] seems to agree with this, given the text description of account suspension implying that it's temporary or for legal reasons (because the account has been used for illegal activity, or to prevent the account's use until it can be restored to its owner in cases where a lock might not suffice)
Admittedly, I have no personal experience with this, nor do I even know anyone who does, but I've never heard of anyone complaining about being unable to play their existing library when banned; complaints about steam tend to be about accounts being stolen and VAC/community bans, with the occasional complaint from someone I know that lost access to an account when they lost their email address and forgot the password (this was before steam had account limitations and steamguard, and they had never bought anything).
My understanding is that your account is effectively made read-only (blocked from purchasing, community, etc) and not removed entirely. Steam's help article on restricted accounts[1] seems to agree with this, given the text description of account suspension implying that it's temporary or for legal reasons (because the account has been used for illegal activity, or to prevent the account's use until it can be restored to its owner in cases where a lock might not suffice)
Admittedly, I have no personal experience with this, nor do I even know anyone who does, but I've never heard of anyone complaining about being unable to play their existing library when banned; complaints about steam tend to be about accounts being stolen and VAC/community bans, with the occasional complaint from someone I know that lost access to an account when they lost their email address and forgot the password (this was before steam had account limitations and steamguard, and they had never bought anything).
[1]: https://help.steampowered.com/en/faqs/view/4F62-35F9-F395-5C...