SYSAUX is the default home for your audit trail. When any tablespace fills up and isn't able to add more space then it will cause errors when data is inserted into it. If your audit trail can't add more records, it could effectively freeze your entire database, prevent logins by anyone but SYSDBA, etc. until you add more storage capacity or delete old records to make room for new ones. Any tablespace that holds tables that grow should never be allowed to reach 100% full.
That said, some tablespaces are set to grow the size of their data files automatically as needed until the disk is full. SYSAUX is usually set this way. Depending on how much space is added at a time, the percent full may hover very close to 100%. Check to see if the data files in SYSAUX are set to auto extend, and how much free space is left on your disk drive, LUN, or storage volume. Also check the max file size for individual data files, which varies depending on your OS and the tablespace block size.