Question: A girl ties up a cat and puts it in the corner. She's not paying attention and it escapes. When she looks in the corner she sees the ropes, and she sees that the cat is gone, and she says "逃げられた".

Is that （猫が）逃げられた = 逃げることが出来た, or is it （私は猫に）逃げられた?

EDIT: Just to clarify, the first one is meant to be the potential form, and the second one is meant to be the passive form.

Answer: 
The latter, passive. 

cf. やられた！
It is 猫に逃げられた, which expresses the fact that the speaker has suffered some damage from the event. 私は can be placed at the beginning but it is not essential. Native speakers would omit it over 95% of the time.

猫が逃げられた makes no sense whatsoever. 

However,　something like　猫がネズミに逃げられた。 makes sense. The cat is the one that suffered damage from letting the mouse go in this sentence.