Refuting error is itself revealing truth, and it will not let you hold on to "emptiness" either.
Sanlun is Madhyamaka in its Chinese form. What it does sounds passive and is in fact thorough to the point of severity: it advances no position of its own and simply takes apart, one at a time, the things you are holding.
At the end it takes "emptiness" apart too. The moment you treat emptiness as a position you can stand on, it turns into the next attachment. That is Sanlun's strongest point and the reason it could not be passed on: it has nothing to sell.
Refuting error is itself revealing truth: no separate "correct position" is put forward. Exhaust every mistaken attachment and that state is itself the correct one. Which means Sanlun refuses to give you a conclusion you can hold. That is its deepest feature and the structural reason it did not survive.
The two truths as teaching: ultimate and conventional truth are two levels of skilful speech rather than two layers of reality. Jizang is extremely clear on the point: the two truths are teaching, not object. It is one of the sharpest divides between Sanlun and the other schools.
The eight negations of the middle way: no arising, no ceasing, no permanence, no annihilation, no identity, no difference, no coming, no going. The eight denials that open Nāgārjuna's Mūlamadhyamakakārikā are the whole method compressed.
By Nāgārjuna. One of the most important works in the history of Buddhist philosophy. Twenty-seven chapters that dismantle substantialising thought layer by layer through negation.
By Nāgārjuna, a condensed version of the Mūlamadhyamakakārikā in twelve approaches.
By Āryadeva, aimed mainly at the specific claims of the non-Buddhist schools.
Usually counted with the other three as "the four treatises". Vast, and encyclopaedic on Mahāyāna Buddhism.
The programmatic work of the school, and the most direct text for understanding Chinese Madhyamaka.
Where the central topics get worked out, the meaning of the two truths and of buddha-nature among them.
This is the fatal point: Sanlun has no system of ritual or practice of its own, separate from the other schools. Its "practice" amounts to using prajñā contemplation to break attachment, carried out in analysis and observation. There is no ceremony an ordinary follower can join, no countable daily office, no technique to hand on.
A school with no practice system of its own has a hard time keeping an order of its own. Once Tiantai (the three interfused truths) and Chan (Zen), which sets up not one thing, had digested Sanlun's ideas whole, there was no need for it to exist as an organisation. That is a peculiar form of success rather than a failure.
This is the most recognisable thing Sanlun has, and the clearest working out of "refuting error is itself revealing truth". Jizang's move is ruthless. Every time you get your footing on one level, he demotes that whole level to conventional truth and sets up a new ultimate truth above it. Four rounds in, you find there is nowhere left to stand.
Hold on to Jizang's most important claim first: the two truths are teaching, not object. They are two levels of skilful speech rather than two layers of reality. Once that is clear, the four levels stop being metaphysics and become a piece of machinery with a definite job.
Ordinary people say things exist, the Dharma says they are empty. This is the two truths in their commonest form, and it is where most people stop.
Stop here and a new problem shows up: you are now holding on to "emptiness".
Both "existence" and "emptiness" get demoted to conventional truth, since they are a pair of concepts that stand only against each other. The ultimate becomes "neither existence nor emptiness".
The trouble with stopping here: "neither existence nor emptiness" is now your new position.
Both "opposition" and "rising above opposition" get demoted, because "I am not taking sides" is itself a side. This is the most refined layer of attachment, and plenty of practitioners are stuck on it and feeling good about themselves.
The first three levels are all demoted to conventional truth. What is left as "ultimate" is no longer another statement. It is running out of anything to say: the road of language cut off, the place where the mind works gone.
Note what this step does: it cancels the format of an answer. It does not hand you a fourth answer. This is why Sanlun says it reveals the truth by refuting error and sets up no truth of its own.
The basics of the two truths, and the common misuses of them (misgrasped emptiness among them), are at section 01 of the coordinates page.
Sanlun flourished for less than a century. It declined immediately after Jizang, and the lineage broke at the end of the Tang.
"Refuting error is itself revealing truth" does not lead anywhere near nihilism. The refutation is there so that you stop settling on any position at all, including the position that nothing exists. Each of the eight negations cuts both ways: not permanent, and not annihilated either.
If you have an appetite for philosophical argument, go straight to the Mūlamadhyamakakārikā in Jay Garfield's translation, The Fundamental Wisdom of the Middle Way, which runs a commentary alongside every verse. It has the highest logical density of any text listed on this site.
Jizang himself is harder to reach. There is no accessible English rendering of the Profound Meaning of the Three Treatises, so in English he has to be approached through scholarship rather than through translation.