Indeed the passive voice of alo with the abl. case can mean what you are aiming for. in L&S:
Hence in pass. with the abl. = vesci, to be nourished or sustained with or by something, to live or feed upon.
It gives classical examples, and this example from the Vulgate (Ex. 16:35):
"... hoc cibo aliti sunt ..."
The 4th dec. ...
In proverbs and sentences, the verb sum is often omitted both as a copula and as a verbal predicate. Font: years of latin in italian schools. Ps: when citing a verb it should be named in indicative present first person singular because that's where we study the root of the verb. and from there we study the endings and irregular verbs. It's a Englishism to ...
Actually, this is not so much a case of missing esse, but of praedicative use of an adjectival word. Adjectives (solus), but also participles, can be used such that they agree with a nominal group (Iulius), while telling you something about the praedicate as a whole (Iulius non [habitat]), not just about the nominal group. This is also possible in other Indo-...
Although it's possible that the verb est has been omitted here, as Adam says, I find it more likely that the sentence really is equivalent to Iūlius nōn sōlus habitat, sed cum Aemiliā et cum magnā familiā in vīllā habitat. Latin regulary uses adjectives in the nominative modifying the subject (and also in the accusative modifying the direct object) where ...
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Est can be ommitted if the meaning is clear. You might want to check out this post about omitting esse, as it's another form of the same verb. In the case of this sentence, it's very clear that the verb is est from both the clause and with the full sentence.
The same happens with all deponent verbs in Latin.
The Latin participle system is defective for a transitive verb like amare:
The gerundive is not really a participle, although it can play roles similar to the present or future passive participle.
I advice against calling ...
As Sebastian points out, there are many ways to say this. His example of sine with the subjunctive is probably one of the more natural ways to do it, Sine, quaeso, ut X faciam.
You can, however, use permitte: Permitte, quaeso, me X facere. Permittere is a rather more concrete verb than sinere, it seems to me. It means to let someone pass (a gate, a wall, a ...