'막히다 (to be blocked, stopped, plugged)' is a verb called ' a passive verb' which is from '막다 (to block)'.
'이/가' is used with '막히다' and '이/가' has an intimate relationship with '막히다'.
e.g. 하수구가 막히다.
What is plugged? --> the drain (sewer) : 이/가 is used as answer to 'who, what, which'
'을/를' is an object marker and is used with '막다'.
e.g. 길을 막다.
--> '길' is an object of the verb '막다'. (What do you block? --> the road)