Well I have done my research & unfortunately, they really ended up their relationship
Here is the press statement from LBH management
Announcement on LBH's News to All the Fans
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Greetings.
This is Player Entertainment
We have an urgent message for all our fans, so we have chosen to announce this in writing here.
Lee Byung Hun and Song Hae Kyo, who have become an official couple for the drama "All In," have now broken up. Having met as the leading characters in the extremely popular drama "All In", the two became lovers in real life through the beautiful meeting opportunity that destiny had given them, and soon blossomed into a couple envied and watched by everyone.
The couple Lee Byung Hun and Song Hye Gyo attended Photographer Cho Seon Hee's wedding in late May as lovers for the last time.
Lee Byung Hun, who is on an extremely hectic schedule of filming movies ("Three Monster" - Director Park Chan Wook, "Everyone has a Secret" - Director Chang Hyun Soo) and in the spotlight as the main actor initiating the Korean wave currently heating up in Japan and Southeast Asia, and Song Hye Kyo, who is busy filming the drama "Full House," have agreed that it would be better for them to remain as "Senior and Junior" as they felt that they are each too busy with their respective work schedules to be able to give the same amount of commitment to their relationship that they had been able to give intially. However, the actual reason has got to be the recent rumors about Lee Byung Hun and Song Hye Kyo's upcoming wedding and how they each had different views towards marriage.
Neverthess, the couple Lee Byung Hun and Song Hye Kyo, the target of much speculation and media publicity, had began to confirm in April that they have both agreed that the love they shared for a year would now remain as just the good relationship shared between a senior (LBH) and a junior (SHK).
Currently LBH is in the midst of filming the movie "Everyone has a Secret" on June 11, and left for Japan on June 14 to attend a meeting regarding production with Fuji TV Documentary and also to discuss the distribution agreement regarding his commemorative album "To Me" with Daichiku Records. Song Hye Kyo too has been busy with the filming of the drama "Full House" and is said to be so busy that she does not have time to think about anything else.
We express our sincere gratitude to all our fans for always supporting Mr. Lee Byung Hun and Player Entertainment. We would also like to ask your understanding for announcing this in writing as we always strive to be the first to bring you any news on Lee Byung Hun.
Player Entertainment