To qualify for the Northern Residents Deduction, CRA says you must have maintained and lived in a dwelling in the northern or intermediate zone to claim the residency amount. "A dwelling is a self-contained domestic establishment". Generally, this is a complete and separate living unit with a kitchen, bathroom, sleeping facilities, and its own private access.

If your care home meets these requirements, then you would be eligible for the deduction. You may want to contact the CRA and clarify if your individual situation meets the requirements.

https://www.canada.ca/en/revenue-agency/services/tax/individuals/topics/about-your-tax-return/tax-re...