Which is correct? Or they are both fine but the meaning is different?
Even if someone you love becomes sick and they may die, you are not responsible for their illness and there are times when there is nothing you can do.
Even if someone you love becomes sick and they may die, you are not responsible for their illnesses and there are times when there is nothing you can do.
So even though it's 'they/their', you have a single person in mind because 'they/their' is pronouns for 'someone (you love)'?
Yes. They/their/them are used as both plural and singular gender-neutral pronouns.
Rover
Very interesting! Thank you!