What is this ni in this phrase?
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The role of 「A には B」 is to pinpoint the location of B at A. Let's compare a direct translation alongside a version with natural sounding English:
The more example sentences you read that use 「には」, the more familiar and natural this will become. Here's another example:
There is an interesting explanation for this use of には included in the following Imabi link.
I've not heard this explanation anywhere before and thought I would paraphrase it and get the community's opinion. It doesn't seem to be commonly held (and is perhaps incorrect?) but it seems to be backed up with actual data.
The author of the site begins his explanation by defining a class of verbs that he calls "stative-transitive" verbs. An in depth explanation of this class is here 第21課: The Particle Ga が II: The Object Marker Ga が .
He describes "stative-transitive" verbs as verbs that describe a state but have a direct object (he takes a rather loose meaning of "direct object" and pretty much extends it to any argument that a verb or predicate complement requires to make sense). He goes on to say that usually, these types of verbs that describe states but require objects are considered transitive verbs or adjectives in English and the analogous verbs in Japanese are considered intransitive or are adjectives.
Examples to illustrate the point are English verbs like "to have", "to like", "to know", "to want to do something" which are all transitive in English while their Japanese counterparts,「いる/ある」「好きだ」「わかる」「したい」are not.
His main purpose in his argument is that he believes it is more appropriate to consider this a special class of verbs in which the semantic object is marked with が. He includes the following table that shows には is often used to mark the semantic subject of stative-transitive verbs when the object is marked with が.
So for your specific example,
彼女には心配事がない = She has no worries.
The ない would be considered stative-transitive because it describes a state but requires an object. 心配事 would be considered the semantic object (marked by が) of the stative-transitive verb and 彼女 the semantic subject (marked by には). It would have presumably been acceptable to have just used は but it seems that including に in these types of cases is about 3 times more likely.