The Joong Ang Ilbo has a gun rundown of events that happened the night President Yoon declared martial law. Even the conservative Joong Ang Ilbo believes illegal acts were committed:

Commander Kwak Jong-geun from the Army Special Warfare Command, center, talks during an interview with Democratic Party Rep. Kim Byung-joo, left, streamed on Kim’s YouTube channel on Friday. [SCREEN CAPTURE]

It turned out that Yoon made direct calls to the commanders of the Army Special Warfare Command and Capital Defense Command (CDC) to confirm the movements of troops. It was also revealed that former Defense Minister Kim Yong-hyun ordered the commanders to stand by even before the martial law declaration and deploy the armed forces prior to the issuance, which could also be seen as an attempt to take control of the National Assembly and the National Election Commission, led by a few figures in key roles under Yoon’s authority. 
  
Based on the testimonies of relevant figures at the National Assembly and media interviews, it is highly likely that the top-secret movements by those chosen by the president were carried out with total disregard for the chain of command, even before the decree came into force. In other words, some illegal acts may have been committed. 

Joong Ang Ilbo

Here is why the martial law attempt failed:

Lieutenant Generals Kwak Jong-geun of the Army Special Warfare Command and Lee Jin-woo of the Capital Defense Command stated that they received a standby order from former Defense Minister Kim Yong-hyun both before and after Yoon’s proclamation of martial law.  
  
They added that Yoon was involved in the process of ordering the movement of troops. This could be an important clue in determining who is responsible for the armed forces deployment as the order bypassed the martial law commander, who has full command in a martial law situation. (………)

“Through a call, I was ordered by Kim to secure the National Assembly facilities and National Election Commission facilities, as well as to mobilize armed forces to control those,” Kwak added in the interview. 
  
The lieutenant general said he was also ordered to pull out lawmakers from the plenary session, but he “did not respond due to the certain illegality.”

The martial law attempt has caused a political crisis in South Korea, but one thing ROK citizens should be proud of is that their military did not go along with this attempt to silence the democratically elected opposition. If Lt. Gen. Kwak obeyed the order and fully sealed off the National Assembly and NEC we might be in a very different Korea right now. Fortunately he did not.

I would think what President Yoon is likely trying to negotiate is an exit where he is arrested by whatever future administration takes power. Over the coming days we should learn more on how this is all going to play out, but for now it looks like Prime Minister Han Duck-soo and People Power Party (PPP) leader Han Dong-hoon are calling the shots for South Korea:

Ruling People Power Party (PPP) leader Han Dong-hoon vowed Sunday to minimize the fallout from President Yoon Suk Yeol’s botched martial law declaration with the president’s “early” and “orderly” departure.

The move came a day after a motion to impeach Yoon fell through due to a lack of quorum, with all but three PPP lawmakers boycotting the vote.

“Through an orderly early departure of the president, we will minimize the chaos for the Republic of Korea and its people, stabilize the political situation and restore liberal democracy,” Han said at the PPP headquarters in western Seoul. 

The party leader stressed that the majority of the public believes that Yoon should step down, as he is unable to govern normally for the remainder of his term.

In what appeared to be an attempt to ease concern among the public and the international community, he said the president will not take part in state affairs, including diplomacy, even before his departure.

Yonhap

You can read more at the link.

Please leave anything you want to discuss in the comments section.

I don’t see how President Yoon stays in power because this is clearly a hint from the PPP leader that they will join the opposition in impeachment if he doesn’t suspend his Presidential powers:

The leader of the ruling party said Friday that President Yoon Suk Yeol needs to be swiftly suspended from exercising power, revealing that Yoon ordered the arrests of prominent politicians during his aborted martial law declaration.

Han Dong-hoon of the People Power Party (PPP) said there is a possibility that the president may again take a “radical” action like the botched declaration of martial law if Yoon clings to the presidential power. 

“Given the newly revealed facts, I believe it is necessary to promptly suspend President Yoon Suk Yeol from his duties to protect the Republic of Korea and its people,” Han told an emergency meeting of the party’s leadership at the National Assembly, referring to South Korea by its official name. 

Han pointed out it was confirmed Thursday that Yoon had instructed Counterintelligence Commander Yeo In-hyung to detain key political figures, accusing them of being “anti-state” forces, and had even mobilized intelligence to detain them. (Yonhap)

You can read more at the link.