The conservative party of embattled South Korean President Yoon Suk Yeol faces a quandary: How do members distance themselves from an unpopular leader without handing a big win to their political opponents.

President Yoon Suk Yeol of South Korea is facing proceedings that could remove him from office after his imposition of martial law plunged the country into a political crisis. Members of South Korea’s opposition submitted a motion on Wednesday to impeach Mr. Yoon. Here’s how the process could unfold.