Yes, you can own a TFSA when you are a non-resident of Canada. Although you do not earn new TFSA room while you are a non-resident, the previously earned room does not disappear.
You cannot however contribute to that TFSA while you are not a Canadian resident. If you do, expect to pay a penalty of 1% per month on the full amount of the contribution until you have withdrawn the overpayment. A partial withdrawal will not reduce the tax calculation.
If you return to Canada, or repay the over-contribution, no further penalty will be assessed. The penalty is not levied on the month you make the repayment – so be sure to make the repayment at the end of the month rather than the beginning of the next month.
You need to fill out an RC423 – TFSA Return, along with a Schedule B – Non-resident contributions to a TFSA. The return is required to be filed by July 1 of the next calendar year.
It is not a good idea to assume that “what they don’t know, won’t hurt them”. Because there are, of course, penalties for late or non-filing of the return that will increase the amount you owe to the CRA.