I would say their friendship is pretty much similar to PriLuvHina who although stronger were definitely crumbling towards the end. However, once they left the show behind they maintained their friendship, Hina even supported Pri against maha bully tv don VIKAS.
They will remain friends outside of the house but yes their friendship is not organic but it will last for sure. The reason it isn't organic is perhaps because they did not like each other initially so sometimes its difficult to digest that this defense of Asim for her is genuine. If i play devil's advocate, Rashami when she was eliminated trashed Asim but when she was all alone in the house, she definitely seeked his support during his divide with Shukla. If we doubt his intention, we can also doubt hers but dude its game OFCOURSE they needed each other, who doesn't?!
That being said Rashami has genuinely grown to love him as a friend now and thinks very highly of him. If Asim has defended Rashami, it can also be that her conflicts gave him the opportunity to rise and come to limelight. This is where she IMO has failed as a player, she never ever took the correct stand for herself as she should have and allowed Asim to dominate. Asim HAS treated her poorly just because of Himanshi, but he will come crashing to Earth soon enough once he sees this woman's antics outside.