Learn English – She being or her being

Mainly on the basis of "grammar rules" more suited to Latin, there are still plenty of pedants willing to tell you accusative pronouns (me/him/her/them) are incorrect in such constructions, and that you should use a nominative pronoun (I/he/she/they).

I suppose the "rationale" for that position is there's a "deleted" verb following the pronoun (more soft-spoken than she is, in OP's example). But you've only to look at the chart in this excellent ELU answer to see that native speakers in general have increasingly abandoned that position, particularly in recent decades. So if you want to sound like a modern native speaker, use the accusative pronoun her here.

TL;DR: I wouldn't go so far as to say she is a "hypercorrection", but it's old-fashioned and stuffy.

I would suggest the following revision. Note: I'm making some assumptions that might be incorrect based on context. It sounds like someone shoved her over a railing of some sort?

The next events passed into the darkness behind her eyelids. Eri let go of the barrier, leaned forward and was shoved violently backward. She tumbled down, ending face up on the floor.

or

The next events passed into the darkness behind her eyelids. Eri let go of the barrier and leaned forward. She was then shoved violently backward. She tumbled down, ending face up on the floor.

She is used when it's the subject of a sentence. Her is when it's the object of a sentence, or possessive.

Subject: She did something.

Object: Something was done to her.

Possessive: Her dog is small.