땅이 꺼지다. Ground sink.
*한숨만 땅이 꺼져라 쉬죠. ( a little correction :))
I don't know this expression is used in English, but if literally translated, the sentence would be "I sigh like ground is sinking." or "You know;I sigh like ground is sinking."
It means he or she sighs with great anguish or with worry.
For reference, "꺼져라." is a rude slang which means "F*ck off." when used alone, (asterisk for masking expletive :))