Refurbished iPhone and AppleCare

Applecare can only be purchased during the active 1 year warranty period.

If it is older, then no.

If the seller did indeed get Applecare, it should be transferrable. Check with Apple's Selfsolve warranty checker by getting the phone's serial number.

Make sure the seller does not owe money on the phone (contract) or to the carrier (outstanding bill) otherwise you will end up with a non active phone.

There is an option given by Apple Care to transfer the plan to a new owner of the phone, contact Apple Care to get more details:http://www.apple.com/de/support/products/iphone.html

10. Transfer of Plan

Subject to the restrictions set forth below, you may make a one-time permanent transfer of all of your rights under the Plan to another party, provided that: (a) you transfer to the other party the original proof of purchase, the Plan's Confirmation, the Plan’s printed materials and this service contract; (b) you notify Apple of the transfer by sending, faxing or e-mailing notice of transfer to Apple Inc.

...

... When notifying Apple of the transfer, you must provide the Plan Agreement Number, the serial number of the Covered Equipment, and the name, address, telephone number and email address of the new owner.

If the seller did any repairs themselves, or had any unauthorized repairs, any and all warranty on that device will be void already. If it is more than one year old, from original retail purchase, the warranty is ended.

EBay sellers are not authorized resellers, so this is no different than any other private party used device sale. Make sure the device is not activation locked, if you can. If it is and the seller refuses to help you remove it, then file a claim with eBay.