"Does the basis include what the employer puts in as well as the employee?"

Basis = money post tax, or already taxed and then invested.

Not typically. Or, Neither, typically. The employer typically puts in money pre-tax (even if they are matching your client's Roth amounts)  and the employee typically puts in money pre-tax (unless they are putting into, for instance, Roth 401(k) ).

No one on the internet knows what your client did or the type of plan the employer offered or how the employee participated.