When I run multiple chains a few behave oddly, for example getting stuck at constant values or drifting to extreme values. Can I throw those chains away and just keep the chains that seem to fit correctly?
No! Markov chain Monte Carlo yields valid fits only when all chains behave the same independently of all others. Those oddly behaving chains are not exceptional, rather they indicate that there are pathological regions of parameter space that the “good” chains just haven’t yet reached.
Unless all chains behave the same your fits are suspect.