What happens when index funds stop being diversified?

"Normal people" have always been told to just invest in the indices--they're sufficiently diversified, winners naturally cycle in and losers naturally cycle out. It's been sold as the low-risk, low-reward way to invest in equities. What happens when diversification stops being intrinsic? We're approaching (if not already there) historic sector tilt in the broad market funds, with commensurately historic concentration in top N companies. The returns have been great, my last 12 months look if anything _too good_ for a basic Bogle-type index fund portfolio. But I know the concentration risk in my portfolio grows daily. When index funds go from low-risk/low-reward to higher-risk/higher-reward what becomes the new "normal people" vehicles?