Maxperson
Morkus from Orkus
Taking a hostage who is dying isn't necessarily all that smart. Their allies may decide that killing the bandit is the most expeditious means to save the ally (since the hostage could easily expire during negotiations).
A readied action to kill the hostage if the party becomes hostile will make that a bit problematic.
Alternately, a simple healing word spell can pull the hostage out of the danger zone (even if the bandit has a readied action, those go off after the triggering action, meaning that the worst thing that happens is the ally is back at zero).
Or dead. If the PC has a single death save failed, the healing word fails. It doesn't work on a corpse.
The party could also promise to let the bandit go, but then kill him anyway. If the bandit tries to take the hostage with them, there's almost even odds that the hostage will die anyway, making it a poor choices for the PCs.
This is a possibility for sure.
Lastly, if they're the more mercenary sort of adventurers, they may welcome the opportunity to split the treasure with one less person. Unless that bandit is familiar with the PCs (in which case he was arguably a fool to fight them) he doesn't know their demeanor.
Maybe, but his sort of group is far rarer than one that actually cares about its members. It's a good bet for the bandit to take.