Learn Hardcore Russian: Её поддерживающий тон вызывает доверие.

Breakdown of Её поддерживающий тон вызывает доверие.

What does её mean here: her or hers? And what case is it?

Here её means her, as a possessive word: her supportive tone.

A useful thing to know is that её has the same form for:

So you have to tell from context and position.

In this sentence, её comes before the noun phrase поддерживающий тон, so it is understood as possessive:

It is often described as an indeclinable possessive form, meaning it does not change for case, gender, or number.

Why is it поддерживающий and not поддерживающая or поддерживающее?

Because поддерживающий agrees with тон.

The noun тон is:

So the participle/adjective-like form must also be:

That gives:

Compare:

So the ending changes to match the noun it describes.