You've dealt with it too many times to count.
And you start judging them.
"get your #### together"
"that is one of busiest people on earth"
"organizational skills? Probably not"
"they've reorged to the point where this is happening at this company"
"he has ceased...caring"
If you notice those hypothetical reactions you could have to a full email or voice mail inbox, you'll notice they are part accusation and part empathy.
The reality is the same - a full inbox can mean a variety of things. The person with a full inbox can be overwhelmed - a white flag if you will that no person could reasonably be expected to deal with the volume and demands they're under. Combine that situation with an aggressive IT policy related to the size of email and voice mail storage, and you'll see the white flag early and often.
Of course, there's a harsher reality at times as well. A consistently full email or voice mail box can mean someone has checked out - part of the issue may be workload, but another part of the issue may be general engagement levels.
How do you tell the difference? My take is that you can usually tell once you have the opportunity to talk with the person - 1-on-1.
The disengaged person isn't going to have much passion or sense of urgency about what they're doing. The simply overwhelmed person, on the other hand, is going to have plenty of passion and still show the spark for what they do for a living. But they're in obvious need of help - the type of help may differ by situation.
Full email and voice mail inboxes always mean something. You just have to talk to the person to confirm what the reality is.