The leukemia would see to that.

[tzfujimino]

The 26-year-old mother looked down at her son who was dying of leukemia. Although her heart was filled with sadness, she also had a strong feeling of determination. Like any parent, she wanted her son to grow up and fulfill all his dreams. Now it seemed to be impossible. The leukemia would see to that, but she still wanted her son's dream to come true. [...]

(Source: Part of the passage named "Bopsy" in an English textbook for Japanese high school students)

What does see to that mean in this context?

 

[emsr2d2]

"see to it" means "make something happen" or "make something come true" or "cause the end of something". Unfortunately, in this case, it's the latter. The leukaemia is going to put an end to her son's chance of fulfilling his dreams.