Let's say a person with a negative net worth dies (no assets, no life
insurance, no pot to piss in, moderate-to-large unsecured debts). Are
those debts then passed on to immediate family members? What if said
family members also have no assets? Are the debts finally written off
at this point?

I am attorney that practices probate law, along with a few other
areas, in Michigan and although our answers do not constitute legal
advice and we specifically disclaim that it may, your question is a
"slam dunk" at least according to the law of the various United
States.

The general rule is that "NO," the decedent's debts (i.e. the dead
person's debts) are not passed on to the family members.

Now, if any person, family member or not, were to have co-signed for
the debt with the decedent, that person would, probably, be liable for
the decedent's debt - although, there are exclusions and defenses.

It may be interesting to note that, on the other side of the coin, if
a person dies owning assets, the heirs do NOT have to take assets from
the estate either.

So, in either case, we are not bound by our deceased relatives debts,
nor are we bound to take their property - unless we want to.

AND, even if someone "told" someone that they would pay the debt of
the deceased, if it isn't in writing that promise has no effect - it
is not binding on the person making the promise.

So, rest easy. And, if a creditor calls - just tell them that "X died.
Don't call again!"

Now, as to whether a probate estate should be opened in the local
probate court - that is a serious question and a difficult question
beyond our scope here.

If you need anything further, please hit the CLARIFICATION button and
I'll get right back to you.

weisstho-ga

This might be different in other places but here in the UK a person's
debts die with him unless some of his friends or family have given
guarantees.

For future questions, it may be best to post a regional or governing
body in which you'd like to check.

Most laws state that a persons debt is not passed on.  (Unless you
were tied to the debt before the decease, joint credit for example). 
BUT, you can still be affected by these debts.  A deceased's assets
may be sold in order to repay the debt.  If the assets don't cover the
full debt at this point creditors will usually have to take the loss.

Google Searches for:
inheriting debt

Sorry my comment came after the answer.  I had begun writing before
the Question was closed and I couldn't post.  I figured I'd just wait
until the question was opened again.