I really was expecting this to end with "to have the disease you contracted cured". It was only when I got to the end of the second sentence that I realised "bites it" here is a term of art!
My own view is that that's not the only way, at least for negotiation. You can also set up fictional situations, in which the players are invested via their PCs, which will be advantaged by negotiating rather than fighting.
But setting up such situations, adjudicating them fairly and effectively, and drawing in the players, is not trivial. It's a GMing skill that can be developed like any other, but good advice can help.
(I don't think that you, CJ, will disagree with much of what follows - though perhaps I'm wrong on that. Rather, I think I'm treating "negotiation" more broadly than you had in mind.)
A simple example: In my game, the PCs fought a Torog cultist and her hired rabble. The rabblee include dockside heavies and wererats. Some of the wererats and one of the heavies escaped. The wererats went back to their base, a ruined temple of Erathis. The heavy went back to the docks. The PCs could easily have tracked down and defeated either or both in battle, but had better things to do with their time - and the players had better things to do to! So the PCs started court proceedings to get the wererats evicted as squatters - which ended up working, but the resolution of the courtroom skill challenge gave me the chance to put in a nice twist concerning the balance of power between secular and religious authorities in the town - and, once they'd retaken possession of the tower in the name of Erathis, defeated the troll, rats and gargoyles that the wererates left behind, and restored it as a temple, the party invoker-wizard tracked down the heavy and hired him as leader of the temple guard and tithe collectors.
Why did the players go this route? Well, they (and their PCs) were getting anxious about the bodycount in the town since their arrival (around 40, in a town of 5,000-odd, over the course of a few days) and didn't want to add to it. They wanted their PCs' re-establishment of the temple to be as legitimate as possible. And the temple is in the docks quarter, and the PCs wanted a reliable guard who would make the temple a site for the projection of power, rather than a victim of others' projection of power.
What are some of the GMing techniques that help lead to the players framing their choices in this way? Showing that death is not the only stakes, by having NPCs run away. Showing that negotiation is possible, by having former enemy NPCs agree to and keep to new terms (the recruitment of the dock heavy as a guard is only the latest such episode in the campaign). Making it clear - by overt communication, as well as practices of adjudication - that the PCs can get what the players want them to get by means that raise rather than lower the esteem of the PCs in polite society (winning court cases rather than killing and terrorising), and making that social context itself matter for subsequent framings of situations - for example, letting the PCs enjoy the modest but real benefits that flow from being esteemed, Paragon-tier saviours of a town.
Conversely, what are GMing techniques that can shut down these sorts of possibilities? Never having NPCs run away or surrender. When NPCs surrender and agree to terms, having them routinely break their promises - or, even moreso, having them routinely betray the PCs (I have seen [MENTION=22779]Hussar[/MENTION] be especially vocal about this in the past). Having NPCs treat even high level PCs as hired rabble of no social consequence (published adventures have from the beginning been rife with this). Making it hard or impossible for the players to achieve goals for their PCs (eg treasure, status, McGuffins, whatever) without fighting for them (eg Gygax advised that NPC wizards will never agree to reasonable terms for sharing spells - this is practically inviting the PCs to slaughter and rob every NPC wizard they meat, in order to power up the PC magic-users!). More generally, making "0 hp" the only measure of finality for the GM: or in other words, the GM behaving as if s/he is free always to reopen some conflict, go back on a settlement, unless it was made final by death of one of the parties.
Some of these techniques are about GMing style. But some - like the issue of finality in non-combat conflict resolution - also go to mechanics.
I've successfully run games where death was common and avoided that pitfall, but it was because I tooks steps to avoid it, not because it wasn't a potential pitfall. 
