Q:

They asked me where I live. Is that question correct?

I know in reported speech we have to change the present simple to the past simple but this question really makes me wonder if I can write it like
They asked me where I live.
Since it's something always true.

A:

You don't have to change to the past tense.
It is correct to leave the tense unchanged. It is more common to leave the tense as present tense when answer hasn't changed since the time when the question was asked.

Yesterday he asked me where I live.
Ten years ago he asked me where I lived.
You already asked me what I am eating five minutes ago.
You asked me what I was eating when I first met you last week.

