Send Bitcoins to anyone via Email & text messages, even if they don't have a bitcoin address or a My Wallet account.
It is as secure as the your email or phone inbox. If your email account got hacked or phone compromised, the attacker would be able to redeem any unclaimed payments.
The private key the funds were sent to is saved in the senders archived addresses. The sender can reclaim the amount at anytime by sweeping that address, it's up to you how long you wait for the amount to be claimed. The address will be labeled "username (Sent Via XX)"
Login to your My Wallet account, click the [Receive Money] tab and then archived addresses. You should find an addresses labeled with the recipient's name. If the address has a positive balance then the amount has not been claimed, sweep the address to reclaim the coins and retry the transaction.