I think #2 is a fairly straightforward “NO!” In fact, I can’t imagine a libertarian interpretation of contract resolution that would make a debt obligation (or any contract, for that matter) binding upon a third party. Debts can certainly be bound to the estate of the deceased, in which case his heirs cannot enrich themselves until the debts are fulfilled, but if the estate is insufficient to satisfy the debtors, they have no right to pursue his heirs for collections.
1 is a fairly complex question, beneath the surface. One is tempted to assume some system very similar to the one we currently have, however, that’s probably an assumption we shouldn’t make. We can probably theorize different debt arrangements than those we have at present. Also, this goes back to the “Caging the Beasts” debate about how Libertopians deal with crime.
I hate having to keep reminding people of this, but they always say that ostracism/etc. won’t work. So, I’ll remind them anyways:
In “Libertopia” all land is presumably owned by someone. These someones have PDAs/Insurance/protection/ Agencies and agreements between them and between themselves and other individuals. Most (all?) of these arrangements would probably prohibit offering safe harbor to fugitives, aiding/abetting fugitives, etc. Also, since many people are afraid of fugitives, it stands to reason that they’d be more than happy to assist in their apprehension. This could easily be accomplished by laying siege to the fugitive if he didn’t want to submit to arbitration/dispute resolution. Fine: he can suffer house arrest in perpetuity. This is easy to facilitate, because land is not public, and those people who live on adjacent lands will likely be unwilling to give him free passage. They, or their agents, will be happy to apprehend him coming or going, or to prevent people from giving the fugitive aid and comfort.
So, the longish-short answer is that it may not be necessary to use “force” as it is contemporarily conceived, i.e., masked men break down the door in the middle of the night, handcuff/hogtie the accused, and drag him off against his will to prison where he’ll be tried by 12 men who were too stupid to get out of jury duty, etc.
They could simply wait for him to arrive upon another’s property, and take him then. Any escalation of force (e.g., “self defense”) by the fugitive is not a proper use of force since he is in-the-act of criminal trespass. Or, they could simply make sure he stays locked in his own house. Most people probably couldn’t survive locked inside their own house for more than a week. Sooner or later, most people would submit to arbitration.