Concatenation of two regular languages
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.