Can `sys.aud$` recycle itself? In Oracle 11, what happens if I leave sys.aud$ to get bloated up to soak up the whole SYSTEM TABLESPACE?

Does it start rewriting the oldest records?  Can Oracle be configured to do so?

Does it stop auditing? Can Oracle be configured to overwrite the oldest records instead?

Does the DBMS crash? It seems not, it will prevent further actions until an operator handles the situation?
The audit table does not 'clean' itself.  And there is not just a simple setting, like an init parameter, to do so.  You have to set up and schedule jobs to do that, and @eckes gave you a link to the documentation.  That same package (dbms_audit_mgmt) also provides a procedure for moving the audit table to another tablespace, getting it out of SYSTEM.  I strongly recommend you do so.  I just create a new tablespace dedicated to the audit table(s) and their indexes.