Episode 2 of "A Killer Paradox" kicks off with a thrilling sequence where a dog hotly pursues Tang, who unknowingly carries a hammer in his bag. Tang jolts awake, initially believing it to be merely a nightmare. He then ventures to his parents' abode, where his mother gently urges him to attend church. As he dumps some trash, a chilling discovery awaits him: the deceased man's head staring back at him from within the garbage bin.
Elsewhere, Nan-gam steps into a flower shop, but the shopkeeper's attention is clearly elsewhere, engrossed in a phone conversation. He subsequently heads to a store, intending to purchase a juice gift box as a token for his father—a retired police officer now confined to bed due to unconsciousness. However, upon realizing it contains two bottles fewer than expected, Nan-gam dumps it in frustration. His mother later scolds him for opting against flowers.
Tang's mother notices his weight loss and fusses over his absences from classes, but her monologue is interrupted by a visit from one of her friends. The trio then proceeds to the church, where Tang's mother offers him a poignant ultimatum: if he wishes to leave for abroad, she and his father won't hold him back. She also hands him a lottery ticket, perhaps as a symbol of hope.
Meanwhile, at the police station, tensions are running high as officers face criticism for failing to apprehend Bu-il before his untimely death. The captain's arrival adds another layer of drama, as he pulls Nan-gam aside and sternly advises him to let go of his obsession with "that guy." It becomes apparent that Nan-gam has been relentlessly pursuing a perpetrator who once wore the badge of honor.
Tang acquires a gleaming new phone and promptly heads to the store, where a part-time female employee is already present, griping about the unwelcoming message on the main door. During her shift, the seemingly blind woman from earlier reappears, demanding that Tang fork over two million won. It transpires that she isn't entirely sightless and is privy to Tang's dark secret—he's a murderer—further hinting that she possesses the incriminating hammer.
At the university, Gyeong-hwan and Mi-young find themselves in deep conversation about Tang's financial pleas to both of them. Tang has even resorted to selling his freshly acquired phone, but to no avail. Desperate, he approaches the store owner, hoping for an advance on his salary for the month. Recalling a previous negative experience, the owner declines his request. Surprisingly, Tang later receives a message from his boss informing him that he's been paid in advance, despite the earlier refusal. Yet, the money remains insufficient. In a moment of utter desperation, Tang raids his parents' house savings account, liquidating every penny.
Repeated calls from Gyeong-hwan and Mi-young go unanswered as Tang remains engrossed in his mission. Inside the store, he clutches a sling bag filled with cash. The owner's arrival, coupled with his mention of the blind woman, prompts Tang to bolt out. He stumbles upon a cigarette box—one he had previously sold to her—bearing a time and address.
At the police station, the captain reprimands Nan-gam for attempting to chase down the suspect out of revenge for his father's demise. Nan-gam, however, insists that he's merely fulfilling his duties.
The following noon, Tang treks to the woman's abode. She greets him with a nonchalant demeanor, brewing coffee and engaging in light chatter while Tang remains tight-lipped. When he withdraws the cash, she reveals a stunning revelation: she meant two million won a month. Producing the hammer, she asserts that she wouldn't jeopardize her freedom by becoming an accomplice for such a modest amount.
Tang abandoned the money, clutched the hammer tightly, and fled the scene. As she departed, she muttered under her breath, revealing her intimate knowledge of Tang's family affairs, which promptly drew him back. She boldly declared that even without the hammer as evidence, the police could effortlessly track him down. Tang envisioned himself charging towards her, like a dog on a leash, but in reality, he lunged at her with the hammer in hand. A splash of blood stained the air as she collapsed, lifeless. In a rush, Tang collected his belongings and dashed out, leaving a trail of crimson on her front door.
Days later, milk cartons began to accumulate at the woman's doorstep, prompting a concerned delivery man to check on her. The subsequent scene was marked by police tape, with Nan-gam and Yong-jae investigating. The woman's body had been severely mutilated, with Rex, the dog, seemingly having feasted on his mistress's remains. Rex continued to create a commotion in the garden, inadvertently revealing a skull buried in the soil.
During the police briefing, it came to light that two skeletons had been discovered in her garden. Meanwhile, at home, Tang found Yeo-ok haunting his every step, contemplating how effortlessly he had taken lives. He had been confined to his home for four days, barely eating, as missed calls piled up on his phone. He pondered why the police hadn't come for him yet.
It transpired that Rex had licked everything Tang had touched in the house, erasing his fingerprints and DNA from the crime scene, foiling the police's efforts. The officers then debated the dog's fate, pondering whether to put him down as a result of his grim involvement.
In the meantime, Tang, consumed by despair, attempted to take his own life but ultimately failed. Sensing his plight, Gyeong-hwan approached and cunningly persuaded Tang to unlock the door. Their confrontation escalated swiftly, with Tang insulting Gyeong-hwan by calling him a fool and confessing to stealing his tablet. Gyeong-hwan, turning the tables on Tang, revealed that he had always been aware of his deceit. This revelation left Tang with a newfound sense of remorse, prompting a shift in his behavior that left Gyeong-hwan thoroughly perplexed about Tang's true nature—whether he was inherently good or evil.
At the precinct, one of Nan-gam's peers was adamant that someone else besides Yeo-ok had been at her residence on that fateful day. However, lacking concrete evidence, their theories remained unsubstantiated. Subsequently, a grim decision was made: the dog, a silent witness to the tragedy, was to be euthanized. The duty fell to Nan-gam's colleague, who was tasked with transporting the innocent creature to the pound.
En route, the dog exhibited an unexpected desire to enter a karaoke bar, where Tang was languishing in a desolate room, still reeling from the aftermath of his recent escapades. His absence from work had not been overlooked, prompting his employer to file a police complaint against him.
Unbeknownst to them, the two mischievous boys from the initial episode reappeared on the scene. They spotted the policeman accompanying the dog and, driven by a mischievous impulse, decided to hassle him. They darted towards him, and one of them delivered a vicious stab with a shattered bottle.
Emerging from his karaoke stupor, Tang caught wind of the shocking news regarding Yeo-ok—she had allegedly murdered her own parents! Meanwhile, the two boys, now wallet-less and wandering aimlessly, caught sight of Tang wandering the streets. Sensing an opportunity to perpetrate their antics once again, they set their sights on him. Tang felt a chill creep up the back of his neck, a chilling sensation that had preceded his previous murders.
The following sight that greets our eyes is a grim discovery: two lifeless bodies sprawled in an abandoned waste heap. As dawn breaks, the detective arrives promptly on the scene to unravel the mystery. Meanwhile, Tang awakens in his home to a startling revelation—he is drenched in blood, as if he's been through a nightmarish battle. Beside his hammer, a brick stained with crimson rests ominously, accompanied by a tiny slip of paper. Tang's memory flickers back, vague but insistent, recalling a shadowy figure carrying him home, yet the identity remains elusive. The note, in concise yet urgent terms, urges Tang to seek assistance if needed, directing him to a Telegram channel named "Only For Heroes," where perhaps, help awaits.