This is the 19176th most frequent Korean word.
안걸렸지
"안걸렸지" means "didn't get caught" or "wasn't detected."
Here, '안걸렸지' indicates negation of the event of catching a cold, confirming the speaker's assumption.
감기에 안걸렸지, 그렇지?
You did not catch a cold, right?
In this sentence, '안걸렸지' expresses the avoidance or absence of being caught or implicated in an issue.
네가 그 문제에 안걸렸지, 다행이야.
You didn't get affected by that issue, that's fortunate.
Here, '안걸렸지' is used to presume the lack of detection in breaking rules in a question form.