When one of your tenants dies, the person living with him/her can in fact become tenant himself. On the one hand, he must continue to occupy the apartment in question and, on the other, he must give notice of this to the landlord within two (2) months following the death [of his/her partner/spouse].
If the person living with the tenant has not given notice to the landlord of his intention within two (2) months following death, then the liquidator of the succession or an inheritor, may, in the month following expiration of the delay of two (2) months, put an end to the lease by giving notice to the landlord one month in advance1.
Indeed, if no-one lives with the tenant at the time of his death, the liquidator of the succession or an inheritor may in fact put an end to the lease. In order to terminate the lease, he must have delivered a notice of three (3) months to the landlord within six (6) months following death. Consequently, he must pay the rent during these three (3) months.
Contrary to popular beliefs, it is important to underline that, in fact, the death of the tenant does not imply termination of the lease2.
1Article 1938 al. 2 of the Quebec Civil Code
2Article 1884 of the Quebec Civil Code