You can close your own account and open a new one at any time: this is not against the site rules. Your stats won't carry across, of course, and if you're trying to circumvent the site rules re: posting of objectionable content, the nof course they'll act on the new account(s) as well.
Chess.com only closes people's accounts if they've done something well outside of the terms & conditions meriting immediate closure, like posting pornography - most of the time people will be warned, and if they don't heed that warning, muted (in the case of objectionable content) or closed (in the case of using engine assistance during actual games). They are pefectly entitled to do this because they make it a condition of joining their web site, so they could close someone accounts for no reason at all, if they wanted to: generally not good business practice, but they'd be well within their rights to do so.
I noticed that a lot of accounts that are closed. For whatever reason, they are closed? Even among my friends, who clearly were very active on the site, now closed accounts. They are free to close your account and create a new one with a different name?