[Corrected from “passive infinitive” to “impersonal passive”. Sorry about the confusion.]
The sentence has no subject because it's an example of a German “impersonal passive” construction.
The “personal passive” is constructed with the passive form of a transitive verb, whereas the “impersonal passive” is constructed with the passive form of an intransitive verb.
In a “personal passive” construction, found in both German and English, the agent of a transitive verb is demoted or omitted from its subject status in active constructions, and in its place the patient is promoted to subject status from its object status in active constructions. For example, the active sentence ‘Sie malt hier die Bilder.’ = “She's painting those pictures here.” corresponds to the personal passive sentence ‘Die Bilder werden hier (von Ihr) gemalt’ = “Those pictures are being painted here (by her).”, in which ‘Sie’ = “She” is the subject in the active sentence, but is demoted to a prepositional object ‘von ihr’ = “by her” or omitted altogether in the passive; while ‘die Bilder’ = “those paintings” is the object in the active sentence, but is promoted to the subject of the passive sentence.
In an “impersonal passive” construction, which has no counterpart in English, the agent of an intransitive verb is demoted or omitted from its subject status in active constructions. For example, the active sentence ‘Sie malt hier.’ = “She's painting here.” corresponds to the impersonal passive sentence ‘Hier wird (von ihr) gemalt.’, roughly translated into unidiomatic English as “Painting (by her) is happening here.” or “There's painting (by her) here.”, in which ‘Sie’ = “She” is the subject in the active sentence, but is demoted to a prepositional object ‘von ihr’ = “by her” or omitted altogether in the passive. The German impersonal passive is often best translated with an English gerund (“painting” in this case), as attempted here, but English gerunds can't really take a demoted agent (“by her” in this case).
In German, the verb is always in second position in indicative sentences, so if the subject is omitted, as it always is in the impersonal passive, something else must take its place — in this example the adverb ‘Hier’. In the absence of an adverbial phrase to stand in for the subject, the dummy subject ‘es’ has to start off the sentence: ‘Es wird (von ihr) gemalt.’ meaning, again in unidiomatic English, “Painting (by her) is happening.” or “There's painting (by her).” However, since the verb ‘malen’ = “paint” can be either transitive or intransitive, this is more likely to be interpreted as “It is being painted (by her).”. Similarly, if the adverbial phrase ‘Bei ihm’ is omitted from the exercise sentence ‘Bei ihm wird gegessen!’, it has to be replaced by ‘Es’: ‘Es wird gegessen!’, which, out of context, would more likely be interpreted as “It is being eaten!”.
In German, this type of impersonal passive is only used in the dynamic passive form, using the verb ‘werden’ — not in the static passive form using the verb ‘sein’. For example, one wouldn't say ‘Hier ist von ihr gemalt.’.