Really, there is nothing about a TN that prevents you from working in Canada, because you don't need any authorization for you to work in Canada (as a citizen).
But what you are suggesting sounds wrong. Do you plan on paying US taxes but not live there? Do you plan on not paying Canadian taxes?
If you are getting a TN to prevent your employer from having to follow appropriate processes for employing people in Canada it feels like you are putting yourself personally at risk for this employer.
Again, I am not an attorney, but you should probably talk to one about options here because something just _feels_ incorrect about this set up.
Edit: I accidently remoted a sentence:
There are many organizations (PEOs) that try to solve this problem, such as https://remote.com/
As a foreign resident, don't pay US taxes unless you're a US citizen. If you don't use a PEO for some absurd reason, you may need to file a 1120F if you're exporting > $100k USD directly and you will have to issue a W8BEN or else your income is subject to a 30% withholding tax at the source.
They want to be an employee of a company in California, while living and working in Canada. This sounds like it's going to be complicated, and a blanket answer of "you don't pay US taxes" seems unlikely to be correct. They're also going to face issues like on day 1 when they walk into the office and they're going to have to go through the whole I-9 thing (https://www.uscis.gov/i-9-central) - waving hands and saying I'm going to live in Canada seems like it's not a solution.
They can't be an employee of a US corporation (as in, a person who gets a W-2, etc).
What they can do is either a) have the US employer set up a Canadian subsidiary that handles their payroll or b) set up their own Canadian legal entity (corporation, sole trader??) and execute a services contract between the two companies. Then they can pay themselves under Canadian rules out of that company, or do whatever plumbers do in Canada -- sole trader or whatnot.
If they're not in the US though (as a Canadian), they're not a resident, and therefore not a "foreign resident".
The entire situation is weird because as we both mentioned elsewhere, the correct approach here is a PEO (or setting up the appropriate hiring organization in Canada), rather than claiming to live (or work) in the US in order to get a TN (either or which would subject them to US taxation), and then claim to not when it comes to taxes.
Why don’t they want to hire contractors? That is what they have to do. You also need to be registered as a business (sole trader at least) in Canada. You don’t need to physically go to California though.
Why are you getting a TN if you will be living and working in Canada? You can work for a US company as an employee without having US work authorization if you are physically outside the US.