Can anyone explain for me the meaning of the phrase "the bed fled"?

Probably cuz we don't say the bed fleed, as that is not only incorrect but a bed that was fleed would be flawed (with flees) just as much as a bed flied would be flawed (with flies).

[Beds, however, don't usually flee (so can't have fled, either) - but no need to look under the bed to figure out what really happened, just start a little earlier in the sentence to see just who took flight and got the heck out of there.]

Okay, the bed was not running away. The bed did not flee.

"occupant of the bed fled"...the occupant of the bed ran away or tried to escape.... FLED...past tense of flee.

"cats...fled" The CATS ran away. FLED...past tense of flee.

I am tempted to ask, "You're just kidding, right?" However, sometimes the simplest little things just will not let themselves be seen. I remember doing a crossword with a friend many years ago. We spent two days and a bit more trying to find a six-letter word for "piston head." Well, on that third day we noticed, much to our amusement, that we had been misreading "prison head." The word was Warden. Ah, well........I hope this helps.

In your two examples, it simply means they quickly left the bed, ran out of the bedroom because they believed they were in danger.

The bed fled...makes no sense.

The peson who was on the bed got off the bed and ran away

The cat = same explanation

The bed is an object it can not fly or run