Your last day of service will be mutually agreed between you and your manager and details sent in writing by Human Resources.
I think it doesn't make sense to interpret this sentence as "the last day is agreed between you, your manager, and details from Human Resources". So, I think "are" is missing for the part "details sent in writing by Human Resources", which means that it should have been written in "details are sent in writing by Human Resources". But in this case, shouldn't there be a comma right before the second "and" since the following sentence is a separate one not sharing the subject?