Failsafe against accidental locking door locks

Hello everyone, I hope someone here can help me. I am looking for a door lock that is failsafe against accidental locking. That is, if the door is locked and closes with you outside, the lock will unlock itself as it is shut. The only way to lock the door would be either lock from the inside while the door is shut or lock from the outside with a key while the door is shut.

What is the name of this type of lock? I tried asking many home hardware stores but no one seems to know what I am talking about. These locks are actually quite popular in public washrooms. Thank you so much.

 

I'm not sure off the name for that lock but installing a deadbolt (without a lock on the handle itself) would accomplish the same thing. Though you would have to lock it from the outside. Not sure what you are trying to accomplish with the lock.

 

Thank you for reading and your input. Its feature is serves the very purpose. With this type of lock, you will never be able to accidentally lock yourself outside. Say for home doors, you may need to break into the house if you lock yourself out. Bathroom doors can lock itself often enough as well. This is particularly important when you are in a hurry.