Unless you have a contract that sets out the manner in which your employment may be terminated, there is an implied term that requires an employer to provide reasonable advance notice of a potential termination. This is what working notice actually is. You are given notice that your employment will end on a date in the future and you are required to continue to work until that date.
The BC Employment Standards Act also provides for advance notice of termination except that the amount of notice required is typically less than the implied contractual term requiring “reasonable” notice described above. In order to count as advance notice, an employer must provide unequivocal notice that your employment will end on a future date. Warnings like “things are not looking good” typically don’t count as advance notice. You need to know that your job will end and when it will end so you can find alternate employment.
In situations where proper advance notice is given, you must continue to work if required. However, your employer must also keep the terms of your employment roughly the same. Substantial changes to your employment during a notice period could give rise to a constructive dismissal. This topic is covered elsewhere in these FAQs. One important point is that the safest play is usually to continue working without suing for wrongful dismissal even if you believe that the working notice period is too short. By continuing to work during this notice period, you will not be considered to have waived your right to sue for a longer notice period once the employment actually ends.