To quietly remove yourself from the madness (they won't even know you're gone!), open the most recent message in the chain, tap the More drop-down menu, and select Mute. Activating this will silence all subsequent messages in the chain, freeing you from the bondage of Inbox Overload.
If you miss something important it's no big deal because muting a conversation doesn't delete any messages. Simply search the conversation's subject line and it'll retrieve every message in the chain (including ones that have been sent since you muted it). And if you want to opt back in to the chain at any time, it's easy: just follow the same steps above that you did to mute, only this time you'll obviously select Unmute.