If I got it right, Lithuanian does have passive participle (neveikiamasis dalyvis). In the case of "while being eaten" it would be "valgomas". "While being beaten" -> "mušamas". He was silent while being beaten -> Mušamas jis tylėjo.

To quote Wikipedia:

    the Lithuanian language is unique for having fourteen different
    participial forms of the verb, which can be grouped into five
    when accounting for inflection by tense. Some of these are also
    inflected by gender and case. For example, the verb eiti ("to
    go, to walk") has the active participle forms einąs/einantis
    ("going, walking", present tense), ėjęs (past tense), eisiąs
    (future tense), eidavęs (past frequentative tense), the passive 
    participle forms einamas ("being walked", present tense), eitas 
    (“walked” past tense), eisimas (future tense), the adverbial 
    participles einant ("while [he, different subject] is walking" 
    present tense), ėjus (past tense), eisiant (future tense), 
    eidavus (past frequentative tense), the semi-participle eidamas 
    ("while [he, the same subject] is going, walking") and the
    participle of necessity eitinas ("that which needs to be 
    walked"). The active, passive, and the semi-participles are 
    inflected by gender, and the active, passive, and necessity 
    ones are inflected by case.