Wow this is an interesting story. This is my take on it: the woman is a necromancer that resurrects Ink every time she dies. Unlike Spiderp (the user above me) I do not think that they are caught up in a loop because of the change in hair color. The woman's current hair is white, but in the flashback she had black hair. This tells us that she has grown older. She does not want Ink to go to the ocean because she is overprotective of her after witnessing her die a lot of times and is afraid that she might drown.
Edit: I wonder if the fountain on the last page is some sort of magical fountain that resurrects people. We can see ashes on the fountain. I assume that the ashes are Ink's. Maybe the woman put her ashes there to resurrect her every time she dies. Maybe the reason Ink is drawn to the ocean because subconsciously she knows the remains of her previous body is out there. Consider this: when asked why she wants to go to the ocean, she says that it might have something to with her previous life.
last edited at Mar 11, 2019 10:12PM