Can a man and a woman live together without marriage?

Islam prohibited private seclusion between non mahram man and a woman and the private seclusion is defined as a place where both are there and a locked door prevents others from walking in and out of the room freely. Prophet Muhammad (peace be upon him) said “no man secludes himself with a non mahram woman without her mahram.
Mahram is defined as a non marriageable male relative to the woman i.e. father, uncle, brother etc… and when the woman is in seclusion with her mahram, this seclusion is not considered prohibited. Based on this understanding if a man and a woman live together in one place where no one else can freely enter then it is considered as a prohibited seclusion and they are not permitted to live alone together.