Nouns that cannot exist by its own, but has to follow some specific grammatical rule.
Example: 지(Noun of uncertainty) can only be used with modifiers(i.e. describing this noun with a verb or adjective).
상황이 어떤지에 따라 달라질 수 있어. (상황이 어떻다 + 지[dependent noun] + 에 따라 달라질 수 있다)
(Things could be different depending on how the situation is.)
The way I see it, 지 when used without a pronoun like '어디'(where) generally stands for an unknown or uncertain thing, whereas 것 usually stands for something that is known. (걸 is just a contraction of 것을).
Taking your second sentence,
아이들은 아기가 자는 걸 몰라요 => The children don't know that the baby is sleeping.
Here, the fact that the baby is actually sleeping ...
To my knowledge, 대 is not a dependent (aka: bound) noun. 대로, 데, 때, and 때문 are though.
Anyways, such a noun cannot be used alone, it must be preceded by a word that describes it such as an adnominal (formed from a verb root with (으)ㄹ, 는, (으)ㄴ, (었)던, etc.), a prenoun (such as 그, 이, 저, etc), among other possibilities.