How can I verify that an investment advisor is not a ponzi scheme if I do not trust the auditor?

The answer to this other question covers how Ponzi schemes are uncovered (and how they conceal their scheme in the first place).

How can Ponzi schemes be detected and legally prosecuted?

You mentioned that it doesn't answer your question specifically, which you noted as:

My question is about what clients can do when the auditor’s reputation is diminished so much that clients can no longer trust it.

From the linked question's accepted answer:

Generally, if an investment fund doesn't have a reputable independent auditor - stay away.

I'll expand a bit so that it's more tailored to your question. The short of it is, there's nothing you can do outside of reading whatever data is made available to you both from the auditors (that you don't trust) and client reviews. If an advisor is running a Ponzi scheme, nothing they make publicly available will show that. That's how the scheme works and why they are sometimes so difficult to uncover. Unless you have access to their closely guarded financial workings, you won't be able to properly evaluate the legitimacy of their operations.

As a "consumer", your options are extremely limited. There are a lot of reputable and trustworthy advisors out there. If you are at all unsure about if you can trust them, then that means you can't trust them. Find someone else.

Auditing firms and auditors in general rarely catch fraud, Ponzi schemes, or related crimes. There are two reasons for this.

First, if I am going to do a financial crime and I am not stupid, then I will do it by following the rules. In the best of all worlds, I will put myself in a position to determine the rules and their implementation. These types of crimes are usually flagged by employees, quite often by accident. I used to know a banker that worked his way up in banking by catching fraud. He was never an auditor, he was just curious. He would ask the questions that don't get asked because everyone is so busy and no rule is being violated.

Second, catching fraud, particularly something like a Ponzi scheme, isn't really their mandate. They are responsible for determining whether or not the books are a fair reflection of the events of the period that they are looking at. That is a subtly different thing.

Because a good financial criminal is following the rules, they are unlikely to be noticed. The original Ponzi scheme, by Charles Ponzi, would have been undetectable unless a seriously diligent auditor that suspected something were to investigate. Had they investigated early enough, they could not have caught it because it was originally done in a legal way.

The original scheme involved what were known as international reply coupons. They were created by the Universal Postal Union to facilitate cross border transactions. The problem was that the treaty called for a fixed amount to be printed per year. His scheme became so large that at some point, he was the owner of all of them. Had he stopped, no crime would have been committed.

The crime worked because the world was on a gold standard. You would buy postage in one country and sell postage in another, but at a different price. Then you would exchange the stamps for gold.

Basically, Charles Ponzi had created something similar to a bid-ask spread for postage.

As you can imagine, since all of the base transactions were legitimate, an auditor investigating the scheme would grant their imprimatur gladly as it was clearly a great idea, if auditors were ethically allowed to do such a thing. It is unlikely an auditor would even notice there was a ceiling. After all, unless you read the treaty or went to buy a coupon, how would you know?

It was only after he ran out of opportunity that he broke the law, but the "inventory" would be in the trans-Atlantic mail in the normal state of affairs. How would you catch it?

There is also the great corn oil scheme of the 1970s. The auditors went to the tanker ships. Dropped in chemical testing containers into the holds of the ships and sampled the oil. The chemists verified they were ships filled with corn oil. The ships were destined to be made into salad dressing.

The problem is that oil floats on water. The oil was several feet deep, but ocean-going tankers are pretty big. The rest was filled with water. Had an auditor performed the math, they would have realized that the ships, collectively, contained more corn oil than was used by the entire industry at the time. However, that was not the job of the auditor.

Their job was to verify grade and quantity. It had not crossed their minds to drop a bucket twenty feet into the hold.

If there is even one chance in one thousand that you are involved with a Ponzi scheme, now is the time to exit. If you even have that little nagging feeling that it may be, then the answer is that it is time to leave.

There are too many credible advisors out there. You are insane to remain there if you have to ask that question. Rule one: do not lose any money!