Finding the base case for T(n) = T(n - a) + T(a) + cn
Every $0\le k\le a$ yields the base case $T(k)$.
If you are trying to solve the big-O of the recurrence, then you may as well assume that there is some $c$ where $T(k)\le c$ for every base case $k$. It will help making the computation a bit easier