What's the prognosis for someone who had head and neck cancer that could not all be removed at surgery?

Depends: Generally not as good as if all the cancer were removed. This one is highly variable based on the exact type of head and neck cancer, its stage, where it was located, and whether additional treatment (radiation, chemotherapy) has been or will be performed. You need to discuss this directly with your otolaryngologist - head and neck surgeon and any other physicians treating you.

Not as good: Unresectable or partially resected head/neck cancer can be effectively treated with combined chemotherapy & radiotherapy in most cases; however, the results are not as good as desired. Generally, it is harder to get a complete response to treatment and often the cancer recurrs locally or spreads elsewhere. Close follow-up is required and long-term survivors in 20-40% cases are present.