Your ability to stay in the property under 'succession' depends on several factors:
- if you were living with them before they died and it was your main home
- if you were living together as a couple/li>
- if you were related to the person who died/li>
- how long you had lived with the person who died/li>
- the type of tenancy they had and how long they had it for/li>
- what the tenancy agreement says - it might give you more rights to take over the tenancy/li>
If you had a joint tenancy, then you can simply stay on living there. However if there has already been one 'succession' you're unlikely to be permitted another.