I'm not sure of your intent with regard to the word "client", so let's use "contract manufacturer" for the company that does the machining.
Per
http://www.fda.gov/cdrh/registration/whomust.html, a contract manufacturer that does not participate in marketing the product they manufacture, whether that product is a finished medical device (i.e. ready to market) or requires further manufacturing steps before it is ready to market (for instance, sterilization, packaging and/or labeling), is not required to register their establishment and not required to list (on the FDA DRLM website) the products they make.
The company that markets the finished product has primary responsibility for all aspects of manufacturing, and is expected to control that manufacturing through their contract with the contract manufacturer.
The company that markets the product has responsibility for premarket notification or approval, as applicable.
The company that markets the product has responsibility for post-market vigilance and any associated reporting requirements.
The contract manufacturer has co-responsibility for those aspects of the product creation process over which they have some degree of direct control, either practically or by contractural agreement. The contract manufacturer may be inspected if an inspection of the product marketer gives rise to questions regarding the manufacturing process, or if a field issue arises in regard to the product they make.