That's an interesting bit of info. I would have thought that the rent must be reported a tax paid on it and I would, until now, have thought that constituted paying taxes. I also thought that it would open the door to having to report and pay tax on worldwide income. If the rent is the total of the worldwide income, I would not have thought in that case that tax was not being paid on worldwide income. Here, the OP says there is no other "worldwide income". Rent from Canada is the only income. But, even having worldwide income (since rent won't count) still might not make one a resident for tax purposes, which is required to collect CCB, as set out here:
https://www.canada.ca/en/revenue-agency/services/child-family-benefits/canada-child-benefit-overview/canada-child-benefit-before-you-apply.html
The OP might have a problem with showing the requisite "residential ties":
https://www.canada.ca/en/revenue-agency/services/tax/international-non-residents/information-been-moved/determining-your-residency-status.html
Another issue that occurs to me is, to the qualify for CCB, one must be a "resident of Canada for tax purposes". I would think one can be that and have no income whatsoever. In that regard, I think I stated the matter incorrectly when I said "one precondition is filing and paying taxes in Canada."
I would expect that to leave the focus on "residential ties". But, only some musings on my part.
I am not sure if
@scylla's opinion, is that no, the OP cannot collect CCB for the kids. She has really only addressed what it means to pay taxes. But that's probably not the end of the matter. I kinda' hazy to me, just like my faltering clarity of expression in this post. At the same time, I remain of the view that CCB was not meant to be extended in cases such as that being posited.