이 끊어지면

if ... is cut off

→ 이
phrase Rare #32,307
if ... is cut off 이 is a subject particle attached to a noun ending in a consonant. 끊어지면 means “if it is cut off” or “if it breaks,” depending on the subject.
KO: 전원이 끊어지면 비상등이 켜져요.
EN: If the power is cut off, the emergency lights come on.

그러다 줄이 끊어지면?

What if the line breaks?

— 크리에이터 (2023)