I am going to assume you are talking about really good AI and not the actual person's consciousness:

I mean, I think it might have some implications of stunting the grieving process for some. It might be unhealthy for some. It might also be good for others. It's hard to say really.

I know there are people I wish I could see again and talk to and hear them laugh. Maybe on their birthday or on a holiday, sit down with some whiskey and pour your heart out. Cry and grieve.

I could also see some Miss Havisham types who would interact every day and lose some sense of reality and get kind of fucked up with it.

Actual consciousness? There would be a lot of issues around legality and personhood. Can a person exist like that and not go insane? That's a tough one.