It could be only several weeks to a couple or few months: once the executor (if there is a will) or court-appointed administrator (if no will) is appointed, he or she can and almost certainly will look to remove you, so the house can be sold or distributed to heirs. If you did not have a written lease for a definite period of time, you can be asked to leave on no more than 30 days notice (possible less, if you were not paying rent; if you did not pay rent, you were a guest, not a tenant, and do not have to get any notice); if you don't leave at that point, they can file the action to remove you.