If Biden does drop out due for a 'health of the party' reason*, I suspect he would endorse Warren. None of the Third Way Democrats are polling all that well to comprise a clear successor, and even the love for the Bootyjudge seems to be fading as people start gravitating to either Sanders or Warren. Sanders is too old and cranky and too "socialist" for Biden to endorse, but Warren has the institutional cred to become a party leader rather than "Old Man Yells at Clouds".
*I can see him doing that if he is winning a plurality of delegates, but not a majority. Biden is old enough to have a very good idea of what happened last time there was fight like that and how it trashed Carter's chances at winning reelection.