Correct, there are limited ways to argue on behalf of property.

The court cases are filed like

US v. $124,700 in US Currency

https://scholar.google.com/scholar_case?case=677960395272430...

Is somebody notified? I guess the property owner knows about it, since it's taken, but is their presence required on court or can the matter be judged while the owner is under arrest?

Civil forfeiture cases are routinely filed in parallel to criminal cases. Criminal forfeiture also exists, which is not being considered controversial at this point in time.

One of the bigger controversies around civil cases is that they are often filed while the owner is not charged with anything.

In both civil and criminal issues, the human is often deprived of the very property they would use to pay a lawyer and help to defend themselves. By design.

Solution is to have stuff that nobody including the state knows about. "I have nothing to hide" well you should.

Ok, so I understand that when there is enough evidence to arrest the property owner, there is also enough evidence for a criminal forfeiture, so my concern up there does not happen in practice.

Also, whatever judgement happens, it's initiated by the owner, so there isn't an issue with timing.

That clarifies a bit how it works.

Anyway, the idea that just having large quantities of money creates strong suspicion of drug crimes that appears again and again on that linked document is beyond disgusting.