If you become a non-resident of Canada, or are considered to be a non-resident for income tax purpose, you can keep your tax-free savings account (TFSA) and you will not be taxed in Canada on any earnings in the account or on withdrawals from it.
No TFSA contribution room will accrue for any year throughout which you are a non-resident of Canada.
Any withdrawals made during the period that you were a non-resident will be added back to your TFSA contribution room in the following year, but will only be available if you re-establish your Canadian residency status for tax purposes.
You can contribute to a TFSA up to the date that you become a non-resident of Canada. The the annual dollar limit by year is not pro-rated in the year of emigration or immigration. Contribution while you are a non-resident will be subject to tax.