I don't think Les Mis will close after the strike, because I bet Cameron Mackintosh has some special event scheduled for the final performance or close to that point. (The last time Les Mis closed he had Frances Ruffelle, Michael Ball (I think), Jennifer Butt (Mme. Thenardier broadway), and a few others join him "to say Au Revior")
And I think RENT has a huge possibility of closing. It doesn't matter how long it's been open, what matters is that its been having trouble selling seats all year minus when Adam Pascal/Anthony Rapp came back for their limited engagement. And it wouldn't suprise me that they made a final attemp to gain some interest in the show and keep it open til atleast Spring. But who knows, I've never been a fan of the show at all.