Deep Down may or may not be dead. The last update we got in 2015 indicated that they were probably starting the game from scratch and we would be lucky to see anything more about it before 2017. Odds are it's in development hell.
With Rime, I don't think it's that the game isn't coming. Apparently the developer, Tequila Works, even tweeted back in March that they had acquired the rights for the game from Sony, which means development has probably extended with intent to go multiplatform like with their first game, Deadlight. Size and scope can really be a detriment to an indie studio, especially one like this where it sounds like they may have sacrificed funding from Sony to avoid being stuck in an exclusivity contract.
I wouldn't say that either are totally gone, but I would expect them to randomly reemerge probably about a year from now as completely reimagined projects.
