Spam filtering is done on several different levels.
ISP level - they try grabbing only the most obvious or malicious payload spam. Don't want to accidentally block legitimate emails.
Heuristic Filter - whichever client you use, as you get spam, mark it as spam. The underlying program will try to find 'keywords' and other identifying features, match them up against other spam, and start either deleting or spam-bucketing emails that reach a certain threshold match on the learned features. I don't like how webmail.cox.com has it set to delete by default, I'd go into your settings and change it to send to the spam folder, just in case it triggers on something you want to keep.
Manual Filter - Here is where you can set up blocks OR other types of filters based on sender address or other criteria. For example, I want all emails coming with from certain organizations/people (status reports etc) skipping my inbox and being filed automatically in a folder. Other senders I've blocked and go immediately to trash or spam. Email bounceback messages go to a specific folder, as certain domains I manage get hundreds of these a day due to spammers.
Sorry if this is a tl;dr - but if you find certain emails to be spam, make sure you mark them as such.
grymwulf, nice textbook explanation but it doesn't explain what is happening with Cox spam filtering.
My wife and I each have a Cox email address set to move identified spam to a spam folder. We have had instances where we received identical email, one was identified as spam the other wasn't. The filter isn't consistent.
Over the last 2 or 3 months, I've found very little in the spam folder and most, 90+%, is ham, valid emails misidentified as spam. I average less than one identified spam a day and, of that, only 0 to 2 a month are actually spam. I have to assume one of two things are happening: 1. I'm not receiving any spam emails, nothing either in my inbox or spam folder. 2. Cox is hard blocking spam coming in and never placing them in my spam folder, in spite of my config to move spam to a folder. I am afraid this may be the case after what happened with Twitter and gmail over the summer. Twitter email wasn't being deliverer anywhere for over a month.
Finally, +1 for Cox not defaulting their spam filter to delete. I have even had a case with my option changed thru no action of my own. Since Cox 1st started with their spam filter I had my account set to mark subject as spam and deliver to inbox. At some point, I stopped receiving anything identified as spam ... checked my settings and they were set to delete, I know I never would select that and I was getting email marked as spam in the past. Somehow it just changed ... switched it to move to spam folder.
What you are describing is what shouldn't be happening, and that's a problem. I don't particularly like the cox web-mail interface (either one of them) - and I particularly dislike having my spam filtered completely away. I don't like doing this, but it might be a better idea to try out an outlook.com or gmail email - that way if you move you don't have to worry about changing email addresses.