System users are stored in the 'DialogUser' table.
There is no column specific to password update. The 'XDateUpdated' column would tell you the last update to the row overall, which would include any changes to the account, including a password update.
Please note that 'XDateUpdated' will not update when using a SQL UPDATE query. It will update when a change is made through Designer, such as password for a system user.
Activate the configuration parameter "Common\ProcessState\PropertyLog" and mark the column "DialogUser.Password" with "Log changes". Following that every change on the password will be tracked and can be shown in history reports.
There is more information about this here: Logging Data Changes
As the change would be made in Designer, there is no process view as in Manager, but you could query this as long as the password is being changed in Designer for the system user:
select operationuser, operationdate, displayvalue from dialogwatchoperation where operationtype = 'U' and displayvalue = 'systemuser'
'operationuser' tells you who made the change.
'operationdate' the date when it was changed
'displayvalue' is the system user being updated.