Your ETA needs only to be valid on the day of entry. Of course, to avoid unforeseen itinerary changes, you should always renew beforehands if you expect to travel to Canada near or after the expiry.
However, the general rule that the passport should be valid for the whole of expected stay (for short-term visitors) still applies independent of eTA (except that the eTA also expires with the passport).
How long can I stay in Canada as a visitor?
Most visitors can stay for up to 6 months in Canada.
At the port of entry, the border services officer may allow you to
stay for less or more than 6 months. If so, they’ll put the date you
need to leave by in your passport. They might also give you a
If you don’t get a stamp in your passport, you can stay for 6 months
from the day you entered Canada or until your passport expires,
whichever comes first.
(Note that no mention of the validity of visitor visa or eTA is mentioned in the FAQ answer)
As explained in the answer to the other question, eTA is only an pre-entry authorization for air travel only, independent of the purpose or duration of the actual stay which is examined at the border and subject to usual rules (e.g. up to six months of stay for visitors).
Assuming you are a foreign national subject to eTA, you would technically need one also even if you have an approved work and student permit (even if you will stay beyond the eTA or passport validity for study or work as it is often the case). The eTA in this case is automatically granted with the approval of the permit, however.
Similar principle applies to visitor visa:
Must I leave Canada by the valid until date on my visitor visa?
No. The date on the visitor visa is the date by which you must arrive in Canada.