My PCs are not murderhobos. Far from it. They are thoughtful and always consider non-violent options to their problems.

Obligation, though, is a different kettle of fish when it comes to problem-solving. Many of the categories of Obligation fall under "perennial" issues, or quirks of personality. (Obsessed characters, for example, will find that they are the source of most of their own problems.) But other problems are easily externalized, not being the "fault" of the PC, and can be locked into one or more individuals. These individuals often have overtly malign intentions towards the PCs (bounty hunters, debt collectors, revenge-seekers).

So, an inevitable suggestion by members of my group who are looking to solve their Obligation woes is to kill the source of the problem. This isn't necessarily a murderhobo-y course of action: after all, Luke & Co. killed Jabba while jailbreaking Han, despite Jabba's presumably "justified" debt on Han and his refusal to accept greater payment.

Now, I'm unwilling to completely "settle" a PC's Obligation to zero if they kill the source of that chain of Obligation. Should they attempt to remove all Obligation by killing its source, I'm very likely as a GM to replace it with "The [FAMILY MEMBER/BUSINESS PARTNER] of [NOW DECEASED OBLIGATION SOURCE] will now [NEW OBLIGATION]."

But I'm still a little conflicted: it's very hard to argue against violence and murder as a solution, despite the obvious domino effects it can have down the road. I'm certainly not looking to institute a "no murder" policy to fixing Obligations, but I'm wondering: how often do you see this used, and do you have any tricks for mitigating its effects?

The bounty on everyone went up after killing jabba, it could be argued that obligation got worse and spread to the rest of the party.

It helps to make the obligation to something bigger than a person.

If the PC is in debt to a local crime boss, make it known that this crime boss answers to black sun (and so will anyone who messes with him). The boss is the face of the obligation, but the PC should know that seeking a bloody way out will lead to much bigger problems. This should be made clear from the start and not just brought up as a reason not to take him out.

Positive obligations tend to work better, usually involving family.

You can spin that kind of obligation in lots of ways, replacing a more PC focussed obligation by using a proxy, and unless your PC is willing to kill his brother/mother/sister/lover it's not easy to get rid off.

But I'm still a little conflicted: it's very hard to argue against violence and murder as a solution, despite the obvious domino effects it can have down the road. I'm certainly not looking to institute a "no murder" policy to fixing Obligations, but I'm wondering: how often do you see this used, and do you have any tricks for mitigating its effects?

Honestly? I don't think I've ever run into it. You make a good point about the demise of Jabba but the capture and release of Solo took up the last quarter of Empire and the entire first third of RotJ. The heroes did try everything they could to break Han out before Leia was forced to kill Jabba. Jabba's death was less an assassination and more an attack of opportunity.

I would only consider mitigating the effects of the death of an NPC on the Obligation if the party put a great deal of time and effort into the course of action resulting in said death. I would also consider keeping the NPC's defenses somewhat nebulous. This would allow you to respond with an appropriately challenging counter-measure if the PCs manage to crack the NPC's lair.

That's easy, the money for the bounty is fronted to an account that pays out regardless of whether the NPC is alive or dead so murder does them no good and likely only accrues more Obligation. Not to mention a bounty type scenario should involve Tiko the Hutt's organization, not just him personally. The debts PCs own should extend beyond anyone personality so that simply killing the person they pissed off solves nothing as someone will assume the mantle of leadership, and it's not good business to leave old debts unresolved.

Options: Pay off the people like the obligation requires; pay off the people, so they look the other way; do something for them to wipe away your debt; offer them someone who is of more worth than you are; in an unlikely situation, bond with them as you have to work together to escape some worse fate; show them unnecessary compassion where they would not, potentially changing their mind; break their legs and the legs of anyone after you but don't kill anyone... eventually they will stop going after you when they realize you will just break all of the legs. that or they will bring out more firepower/larger numbers.

That's easy, the money for the bounty is fronted to an account that pays out regardless of whether the NPC is alive or dead so murder does them no good and likely only accrues more Obligation. Not to mention a bounty type scenario should involve Tiko the Hutt's organization, not just him personally. The debts PCs own should extend beyond anyone personality so that simply killing the person they pissed off solves nothing as someone will assume the mantle of leadership, and it's not good business to leave old debts unresolved.

A revenge fund, yes very good idea.

I have a question about Obligation.

An obligation is triggered for the session, but due to the nature of it, it is impossible to resolve it during one session. How do you handle this? Should the strain penalty be lifted up the moment the PCs start "attending" the Obligation and after that there is an Obligation roll again or the old result is kept until the situation is resolved which may take a long time?

For example, a Debt obligation is triggered (obligation shared by the entire party). The Hutt to which the group is indebted sends the party to steal the Jewel of Yavin gem to pay the debt off. Obviously the group is not going to handle this matter in one session. Do we keep obligation until the steal the gem or the moment they step on Cloud City and start doing the job, the obligation penalty is lifted and on another session we roll another obligation?

RAW, obligations triggering and the narrative consequences do not have to be in the same session (pg 307, "using the obligation check", 2nd half of 2nd paragraph). The strain penalty though, lasts for one entire session when it is rolled. In your example, the PCs would take the strain hit the session they were given the job, but next session it would be gone unless it was rolled again.

I think you answered your question in your equation sentence. The structure of the underworld - and forces of government opposed to the underworld - ensures some kind of consequence from damage or power vacuum.

In reality, that's bleak, but in an antihero adventure, it means a fresh storyline.

Don't forget, that players should always be resolving and gaining obligation. There starting obligation maybe something they take with them the entire span of their character but they may also resolve that story beat and move on. During their adventures they should be incurring more obligation and that should be adding to their obligation score. I don't believe I've ever ran a game where my players didn't occur some obligation (added to their score) to the Empire either by getting caught doing criminal activities or fighting and killing imperial troops.