I .
to become thinner, for example as a result of eating less
II .
slim down | ˌslim sth ↔ ˈdown
to make a company or an organization smaller, by reducing the number of jobs in it; to be made smaller in this way :
They're restructuring and slimming down the workforce.
The industry may have to slim down even further.
the new, slimmed-down company