For the mobile, it creates some confusion. Essentially, as David mentioned, the mobile phone is a supplemental card. It's like having two cards: one is in your phone, and you have your physical card in your physical wallet.
If you lost your phone, the situation is actually no different from that of losing your physical card. You follow the same process: you contact your bank and alert them that the card has been lost. You're covered by zero liability; they'll issue you a new card number; then there is the provisioning that has to be put onto the new handset. It's really as simple as that; it's like having an extra card.