Q:

Concatenation of two regular languages

In a question, it is given that L is a finite language over the unary alphabet and L+ is not regular.
We know that L+ = LL*
Since L is finite, it must be regular because all finite languages are regular.
If L is regular L* is also regular.
Then how can be L+ not regular? It is the concatenation of two regular languages. Where am I wrong?

A:

it is given that L is a finite language over the unary alphabet and L+ is not regular.

That's impossible.  Since $L$ is finite, it is regular.  Since $L$ is regular, $L^+ = L L^*$ is regular.  See, e.g., https://en.wikipedia.org/wiki/Regular_language#Closure_properties.
You're not wrong; you are right.

