Step 1: Think of the life table population built from a fixed radix $l_0$ and fixed age specific survival numbers $l_x$ that never change from year to year.
Step 2: Since the same number of people enter at age 0 each year and the same numbers survive to each age $x$ every year, the numbers in every age group, and hence the total population $\sum l_x$, stay exactly the same year after year.
Step 3: Such an unchanging life table population is, by definition, both constant in size and constant in age composition.
Step 4: This textbook life table population is what demographers call a stationary population, as opposed to a stable population which only fixes the composition while size may still grow or shrink geometrically.
\[ \boxed{\text{Stationary population}} \]