Draft -- Defunct email addresses from your LinkedIn account  (Jul 27, 2017.)

Check for defunct email addresses -- such as former employers or old email services -- in several places on your LinkedIn account. Otherwise, LinkedIn is probably sending useful emails -- for things you specifically signed up for -- to your old address. (For example, if now at HPE, DXC, or Micro Focus, you must check in several places to ensure that LinkedIn isn't sending emails to your old @hp.com address.)

Changing the main address on your LinkedIn account is not sufficient. Due to a design bug, LinkedIn is still sending emails to former addresses, such as @hp.com, via LinkedIn groups. Here's how to "powerwash" your LinkedIn account:

First, recheck your main settings. Hover over your photo in the top right corner of any LinkedIn page. Select "Privacy & Settings" then "Email addresses."   don't want to remove addresses people know you by

For most people, your primary address on LinkedIn should be a personal account. Why? Continuity through changes in employment. Privacy. And to avoid emails being inadvertently discarded by your current employer's firewall. LinkedIn never exposes your email address. Each message you send via LinkedIn -- and each message sent to you by a colleagues, recruiter, group, etc. -- uses a LinkedIn email address with a unique random message number.

Second, powerwash your group memberships. Go to https://www.linkedin.com/groups/my-groups For each group, use the gear icon to select "Group settings." Due to a design error by LinkedIn, it turns out that the "Contact Email" is the primary address that was on your LinkedIn account at the time you joined that group -- which may no longer be valid. (Group managers -- such as the HPAA team members who manage  the groups we run like Hewlett-Packard / HP Inc / HPE -- cannot fix this.)  With the down arrow, select the desired address from the list of current addresses on your account. Save Changes.

see also post on experts re LI not reaching

a. "Send me an email for each new conversation" currently has no effect.
b. "Send me a digest of all activity in this group" causes a random subset of posts to be included in an single email every week or so. Does not include all activity.
c. "Allow the group admins to send me an email" controls the [New announcement] emails.