They don't come to anyone.

Eventually, people come to them.

Being intractable and stubborn and dogmatic is what it means to claim your fealty to the R or the D side. Variance is not allowed. (Post Bill Clinton, at least.)

Did Hillary do a single thing to bring Bernie supporters into the fold? To appease them in any way at all?

Nope. Nada. Zilch. She didn't have to. Her company had control over the party purse strings, and simply pulled them shut.

"Grassroots candidates" are a convenient fiction. People like Randy Bryce show up now and then, but they aren't connected to the right people or channels, so they can't leverage any of the existing infrastructure that the parties have in place.

Political parties are industrial-era machines. Letting a little guy come poke his head up from time to time is good for the morale of the electorate, and makes us think we have some power or input into the process. So the parties let them percolate up, maybe bring a specific issue to light, and then switch the narrative away from the little guy and back to the party-approved candidate.

No matter how far down the rabbit hole you go, it's dollars, all the way down.