Could it be that the team makes the running back not the other way around? They might not have fit as well into the teams they went to vs. the teams they were on.
The conventional wisdom over the past few years has been that running backs aren't worth paying high salaries: i.e. they're highly replaceable.
@grayruby's idea was that the teams that signed them recognized that they were particularly good fits for what those teams needed out of the position. In other words, their marginal value is higher on their current teams than it was on their previous teams.
That would also be a good reason to take them on, if they were good fits for the team. Conventional wisdom is often incorrect. I think the marginal value argument, which is much like the Moneyball argument, is more likely correct. Also, perhaps it takes some time to acclimate to a new team. I don’t think that that a team would either trade a way an excelllent player or take in a player unless it was in their best interest (more winning games). I guess we shall see in the future.