She'll continue adopting the softest of his policies to take some of the wind out of his sails (as he is doing with her; at the Madison event, he actually discussed police brutality and broke down youth unemployment by race) as long as the polls show what they currently show. She's not going to alienate Wall Street because she believes what they believe largely on economic matters, not because she's afraid of losing their money. In addition, nobody who might vote for Sanders would honestly believe Hillary had a sudden, leftward change of conscience.
If/once he begins to close in even more, then she will do what the Clintons always do when put in a tough position: scorch the earth. Yes, she herself might not do it, but anyone with a lick of sense or political awareness will know damn good and well it's Clintonland. Of course, this will indicate to the world that she is genuinely vulnerable and afraid (and in a real way - not that whole "we're not taking this for granted" series of talking points we heard from the campaign at the onset).
Remember, however, that Clintons not only survive, but thrive in controversial situations. The only reason Hillary Clinton isn't President today is because of a technicality where two states screwed themselves out of being able to seat their delegates (and had the Clintons been able to know just how close it was going to be throughout the entire primary beforehand, those states would have fallen in line in 2007).
Sanders cares about police brutality and racial inequality more than Clinton. He is saying these things because he believes them, not just to counter Clinton. If anything, he cares more about this issues than she does. He talks about them whereas Clinton only talks about them to say "Sanders isn't talking about them" (which again, isn't even true).
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