Of course it's possible. It's the same as sending someone a message. It's just not secure because I too have a copy of the key pair and it'll be a race to see who can move the coins first. Private keys are called private for a reason. You don't share them!
Now if I can somehow prove to you that I don't have another copy of the private key then it will be secure. Being able to prove you don't know something is very hard though
Opendime came up with a concept around it that relies on hardware features. But I'm sure someone will come up with a way to crack an opendime without it being apparent that he has done so.
Another concept is to lock the coins in a multisig address and exchange unsigned transactions with the other party. This is the idea behind lightning.