I think the same way, that the situation will be mirrored in a sense. But could the negative house edge be set in such a manner and value that would still allow the house to profit without turning into a Ponzi and lying about its real house edge (for the sake of getting a competitive edge over other dice cites)?
The only way is if the house edge isn't fixed, I think. It could change so as to keep a small fixed profit for the casino. So if the casino was lucky in the last bets, the edge could go to negative. If the house lost money, the edge could be positive. But I think many people would not play when the edge was positive to the house, and only when it was negative xD
That would be a really good marketing idea. Regarding people not playing when the edge would be positive to the house, I don't think that will be the case (to any significant degree, at least)
First, if the house edge would frequently change in a small range (and with a good bankroll this is what we could safely expect), say, from +0.1 to -0.1, this wouldn't make a difference to most players, which are driven by adrenaline, not by house edge. Second, if people play at dice sites where house edge is set to around 1% positive, why would they not play when it is set (or, rather, fluctuating) way below that? Indeed, some people would evidently wait for the house edge to turn negative, but their numbers should be small...
And the real house edge could be revealed only after the bet has been made