To the algorithm they use in this study, it counts as a failure unless the company is public, which is my point here.

To investors, whether an investment is a success or a failure is indeterminate till the company either goes out of business or returns the capital invested.

when the company is profitable and has valuation, the investors can sell their shares. If the investor makes a profit by selling their shares, will it count still count as failure? It is possible that the investor can lose money, even if the company goes public, right?

I don't understand what you're asking. Can you try again?

Lets say an investor puts 3M for 30% of the company. 1-2 years later, X is profitable and valued at 30M. Now, if the investor sells their 30%, they will make 9M. That is 6M in profits.

Is this considered as success? It is not an IPO or big acquisition. But, the investor can make money by selling their shares.

Is this something the investors consider doing?

In practice it is very difficult to sell shares of a private company.

"self sustain" is a complicated concept

It can mean "ramen profitable" or something slightly better (like it can pay the rent and the founders a small salary)

Either way, not good. You don't need a home run, but you need something that can "fly for itself""

Getting there is tough, most startups are like making a rock fly

Assuming it's actually making good money not just breaking even, its true valuation will be high (though it can't be measured using the 'latest round' method)