According to Imabi
Passive and the potential is impossible. ...Even if it does sound feasible, ～ことができる would be the closest match.
Japanese doesn't allow grammatical items to be doubled next to each other, even if they are used for different things.
The passive is natural intransitive. "To be able to (happen)" by nature is also intransitive.
The passive in English and Japanese results in an intransitive phrase, and it means a lot for grammar. When you double られる, you break two rules of Japanese grammar 1. You're doubling the same think. 2. You're doubling transitivity. Though there are instances where this is allowed for semantic reasons (like transitive + causative), Japanese runs away from dealing with the issue for the most part.
Potential is already structurally similar to the passive. You can see this in how the particle changes from the object marker を (wo, o) to the subject marker が (ga).
Tora wa shika o korosu.
As for tigers, kill deer.
Tigers kill deer.
Tora wa shika ga koroseru.
As for tigers, deer can be killed.
Tigers can kill deer.
Watashi wa sushi o taberu.
As for me, eat sushi.
I eat sushi.
Watashi wa sushi ga taberareru.
As for me, sushi can be eaten.
I can eat sushi.
Note: for ichidan verbs, you can distinguish who did the action in a passive sentence by using the particle に (ni).
Sushi ga watashi ni taberareru.
Sushi is eaten by me.
Note: を (o) may sometimes be found in potential expressions, but is not standard grammar. It may also be found in passive expressions to indicate the suffering passive.
Given that the basic syntax of a potential expression is so similar to that of a passive expression, it's not possible to combine them without sounding extremely awkward. It would be much simpler and better sounding to rephrase it.
Shika o korosu koto wa dekiru.
Shika o korosu koto wa kanou da.
Shika o korosu koto wa arieru/ariuru.
Killing deer is possible. / It is possible to kill deer.
References for the other common ways to say that something possible - koto ga dekiru and -eru/-uru
Yet another common way to say that you're not sure about something is -ka mo shirenai, literally "can't even know if (preceding phrase)."
Shinu ka mo shirenai yo!
(You) could die! (Equivalent to "You could be killed!")
History: the similarities between the passive and potential forms exist because originally godan verbs also used -areru for potential as well passive. source1 source2 source3 One of the sources also states that -areru originally came from the auxiliary verbs -aru and -eru, the latter of which expresses potentiality and can still be commonly found in constructions such as "arienai" (impossible, literally "can't exist").