Erasing Sol's existence to Sunjae's memory is unnecessary.
If Sol knew this or if Sol figured this out, maybe she no longer needed to erase herself from Sunjae's memory. If that happens, then we will have shorter version of Lovely Runner or maybe more fluffs.
Here I go. So first, let's talk about timelines. I separated the timelines into five.
OG Timeline - In 2023, Sol is paralyzed from the "accident". Sunjae was depressed and filled with guilt; Geum did not pursue his dreams and he became snobby and unhappy. Sol and Geum eomma have a burnt scar; Hyunjoo is single and her life revolves around Sol; and lastly, Inhyuk has a strained relationship with Sunjae, his best friend.
First jump timeline- In 2023, Sol is still paralyzed and Sunjae is still dead. However, unlike the original timeline, the photo booth picture, which was taken after Sunjae's match appeared at the crime scene.
Second jump timeline - In 2023, Sol remembers her missing memories from a traumatic experience. Sol is no longer paralyzed and Sunjae is alive. Sunjae and Sol dated for a day then Kim Young Soo attacked Sunjae and got comatose.
Third jump timeline - No version of 2023 since Sunjae died in their first year of college and Sol travelled back in time.
Fourth jump timeline - In 2023, Sol is alone. Taesung became a cop and Sunjae no longer remembers Sol. *The rest is history*
Let's discuss what I mean about this. If only she knew this, then the amnesia trope would not happen.
Before I begin, we can all agree that Kim Young Soo is just a psychopath who kills and never lets go of his prey. Once he has taken an interest in you, he will chase you as long as he can reach you. Sol is the unfortunate victim. She was in the wrong place at the wrong time. In my understanding, the victim of Juyang Reservoir incident should have been Im Sol. However, she escaped and lost her memories due to trauma. It was portrayed as a car accident because that's what only Sunjae knew. Since he was the sole witness of the incident despite not knowing what really happened, Young Soo still saw him as a threat. This is why he was the first one Young Soo killed in 2023 because Sunjae is the sole witness of what happened to Sol despite only knowing it was a car accident. (Assuming that Sunjae did not kill himself)
Sol really has no idea what has happened. She accepted the CEO's statement that Sunjae killed himself that's why in her first jump, she only focused on saving Sunjae (and might as well avoid the car accident). However, when she returned in 2023, she was still paralyzed but Sol can change the timeline and as proof, the non-existent photo in the original timeline appeared in the first jump timeline of 2023. However, that still doesn't change that Sunjae is still dead.
In the second jump timeline, Sol missed her bus stop and stopped at Juyang Reservoir because she overslept. This is where she got some of her memories about the abduction. She realized that Sunjae saved him. When she was waiting for the taxi, a taxi cab appeared out of nowhere. The driver saw Sol alone in the bus stop and when he was about to approach--a drunkard appeared and pestered Sol. Thanks to that drunkard--the taxi left. When Sol tried to get away from the drunkard, Sol fell into the water and lost her phone where Sunjae saved him, she remembers how Sunjae saved her in the original timeline, After that, Sol lost her phone and we never heard of that drunkard. The next day, a dead body in the Juyang Reservoir appeared. (It was said that is an angler or a foreign angler and the drunkard looks like an angler)
This incident is what I call the "meeting point". Sol never changed this part that's why the 2023 of her first jump timeline left her paralyzed because innocent Sol was meant to miss her stop, get abducted, escape, and get saved by Sunjae. The second and third jump timeline was the continuation of Sol's first jump timeline.
The reason why they were hunted by Young Soo--Sol became the prey of Young Soo and Sunjae, being the guy who is always there for Sol became a threat to him. As long as the meeting point of Sol and Young Soo never changes, Sol will always be hunted and killed.
To solidify this theory, in the fourth timeline where she can no longer travel back in time since Sol never took the watch of the dead Sunjae in the third jump timeline, like how Sol evaded Sunjae; she may also evade the Juyang Reservoir that's why she was not hunted by Young Soo. If she knew that she just needed to evade Juyang Reservoir and the driver then, she no longer need to erase herself from the memories of Sunjae.
Like how Sunjae said to Sol, (not word for word but) "the reason why fate does not change is not because it is inevitable but because that person likes the decision." This applies to Sunjae and Kim Young Soo.