Technically, it exists, but as a Japanese-speaker, I would NOT recommend that you actively use it --- at least not on a regular basis.

As @Chocolate stated in the comment above, 「～～させられうる」 is the form. Your sentence “It is possible that she may make you eat her cooking.” can be said in Japanese as:

「ボクは[彼女]{かのじょ}に[自分]{じぶん}の[料理]{りょうり}を[食]{た}べさせられうる。」

This is 100% grammatical with the 6 kana at the very end expressing exactly "causative, passive and potential" in that order.

Is it something native speakers would say in a natural setting then? No, not at all. It would not only sound very awkward but also lend itself to misunderstanding by the listener or reader. "Three different elements in just 6 kana" is too much cramming, leaving no room for mis-hearing or mis-reading even one of the six syllables.

It would look/sound much more natural if you said:

「彼女に自分の料理を食べさせられるかも[知]{し}れない。」 or

 

「彼女に自分の料理を食べさせられる[可能性]{かのうせい}がある。」

What I did was to use other words （かも知れない and 可能性がある） to express the potentiality without relying exclusively on the verb and auxiliary verb conjugations to express all three elements (causative, passive and potential). The 「食べさせられる」 part only expresses causative and passive.

Technically, it exists, but as a Japanese-speaker, I would NOT recommend that you actively use it --- at least not on a regular basis.

As @Chocolate stated in the comment above, 「～～させられうる」 is the form. Your sentence “It is possible that she may make you eat her cooking.” can be said in Japanese as:

「ボクは[彼女]{かのじょ}に[自分]{じぶん}の[料理]{りょうり}を[食]{た}べさせられうる。」

This is 100% grammatical with the 6 kana at the very end expressing exactly "causative, passive and potential" in that order.

Is it something native speakers would say in a natural setting then? No, not at all. It would not only sound very awkward but also lend itself to misunderstanding by the listener or reader. "Three different elements in just 6 kana" is too much cramming, leaving no room for mis-hearing or mis-reading even one of the six syllables.

It would look/sound much more natural if you said:

「彼女に自分の料理を食べさせられるかも[知]{し}れない。」 or

「彼女に自分の料理を食べさせられる[可能性]{かのうせい}がある。」

What I did was to use other words （かも知れない and 可能性がある） to express the potentiality without relying exclusively on the verb and auxiliary verb conjugations to express all three elements (causative, passive and potential). The 「食べさせられる」 part only expresses causative and passive.

Technically, it exists, but as a Japanese-speaker, I would NOT recommend that you actively use it --- at least not on a regular basis.

As @Chocolate stated in the comment above, 「～～させられうる」 is the form. Your sentence “It is possible that she may make you eat her cooking.” can be said in Japanese as:

「ボクは[彼女]{かのじょ}に[自分]{じぶん}の[料理]{りょうり}を[食]{た}べさせられうる。」

This is 100% grammatical with the 6 kana at the very end expressing exactly ";causative, passive and potential" in that order.

Is it something native speakers would say in a natural setting then? No, not at all. It would not only sound very awkward but also lend itself to misunderstanding by the listener or reader. "Three different elements in just 6 kana" is too much cramming, leaving no room for mis-hearing or mis-reading even one of the six syllables.

It would look/sound much more natural if you said:

「彼女に自分の料理を食べさせられるかも[知]{し}れない。」 or

「彼女に自分の料理を食べさせられる[可能性]{かのうせい}がある。」

What I did was to use other words （かも知れない and 可能性がある） to express the potentiality without relying exclusively on the verb and auxiliary verb conjugations to express all three elements (causative, passive and potential). The 「食べさせられる」 part only expresses causative and passive.

Technically, it exists, but as a Japanese-speaker, I would NOT recommend that you actively use it --- at least not on a regular basis.

As @Chocolate stated in the comment above, 「～～させられうる」 is the form. Your sentence “It is possible that she may make you eat her cooking.” can be said in Japanese as:

「ボクは[彼女]{かのじょ}に[自分]{じぶん}の[料理]{りょうり}を[食]{た}べさせられうる。」

This is 100% grammatical with the 6 kana at the very end expressing exactly ";causative, passive and potential" in that order.

Is it something native speakers would say in a natural setting then? No, not at all. It would not only sound very awkward but also lend itself to misunderstanding by the listener or reader. "Three different elements in just 6 kana" is too much cramming, leaving no room for mis-hearing or mis-reading even one of the six syllables.

It would look/sound much more natural if you said:

「彼女に自分の料理を食べさせられるかも[知]{し}れない。」 or

「彼女に自分の料理を食べさせられる[可能性]{かのうせい}がある。」

What I did was to use other words （かも知れない and 可能性がある） to express the potentiality without relying exclusively on the verb and auxiliary verb conjugations to express all three elements (causative, passive and potential). The 「食べさせられる」 part only expresses causative and passive.