Gittin 39 - Freeing one's slave

If a master makes his slave ownerless, the slave is free, but requires a letter of emancipation (Get), because he did not acquire himself.

However, when a convert dies without children or wife, his adult slaves go free and do not need a Get, because they become their own masters, then free themselves.
A slavewoman begged her dying master to free her. He threw her a hat intending for her to acquire herself through "exchange". But he did not achieve anything - not because a letter of emancipation was still needed, but because the hat was his.