What is the function of "달려" in this sentence: "엎에 주머니가 두 개 달려 있다" ?
Does it still make sense if you remove it?

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달려 있다 = 달리- + -어 있다

있다 here is used as an auxiliary verb, meaning “something is keeping/assuming the state of the main verb (달리다 here)”. It requires the ending -아/어/여 to be attached to the preceding main verb. E.g.,

앉아 있다: someone is seated
서 있다: someone is standing
죽어 있다: something has been dead etc.

달리다 here is a different verb from the usual “to run” 달리다. This 달리다 is a passive version of the verb 달다 (to attach/adorn/sew/hang/put something onto something else).

So 달려 있다 means “something was attached and is kept ever so”.

엎에 주머니가 두 개 달려 있다: It has two pockets sewed on its side.