In most states, as long as a process server leaves the paperwork at your home with an actual person (not a child), they don't have to actually leave the paperwork with you. I would check the local court rules of civil procedure to be sure, but avoiding the process server typically means that you will be served by an allowed substituted method that will leave you unlikely to actually hear about the service in time to defend yourself. Hope this perspective helps!
If the process server is not able to serve you but can determine that you are likely living at the address they have (which is sounds like he has), the Credit Card Company (or debt buyer) can ask that the court allow for alternative service. If the court approves this request (and most times they do), the process server only has to deliver the summons and complaint to your residence and mail another copy to you. The court will accept the posting as service, and if you do not respond, will issue a default judgment against you.
You should consider consulting with a debt defense attorney and possibly a bankruptcy attorney asap.
The process server may also be able to serve you by handing you the paperwork even if you refuse to accept it, if he feels that he has sufficient information to show that you are you, he would file an affidavit with the court describing the person he served and the court will likely accept that as proof of service. The court case would then move forward and if you did not answer a default and default judgment woudl be entered. It will be difficult to say that you were not served, without committing perjury in that case. Also, the debt collector can ask the court to authorize alternative service - by publication, by mail, if you are attempting to evade service, which if authorized is also effective service. You can move, but that does not prevent the debt collector from requesting, and may not prevent them from obtaining permission for alternative service.
This information is provided for general informational purposes and is not intended as legal advice. An attorney licensed in your jurisdiction can answer questions specific to your specific fact situation and provide you appropriate advice as necessary based on the specific facts of your matter and the jurisdiction in which you reside. If you are in Arizona and interested in discussing your matter further I can be reached at: (480) 838-9000 Mark D. Fullerton, P.C. 1839 S. Alma School Road, Suite 275 Mesa, Arizona 85210