Concerning the construction venire + participio passato things are a little bit more weired. Let's recapitulate.
The passive with essere + participio passato in the presente is always a static passive.
Io sono eletto.
I am elected (not: I am being elected.)
If one really wants to describe a process, but not the result of a process, a state, one should use the structure venire + participio passato.
Io vengo eletto.
I am being elected. (not: I am elected.)
Io venni / venivo eletto.
I was being elected. (not: I was elected.)
In the case of the presente or the imperfetto essere can't be substituted by venire without changing the meaning of the sentence.
dynamic passive, describing a process: Io vengo eletto. <=> I am being elected.
static passive, describing the result of a process: Io sono eletto. <=> I am elected.
In the compound tenses (passato prossimo, trapassato prossimo) the construction venire + participio passato can't be used. The construction venire + participio passato can only be used in the simple tenses.
correct: Io sono stato eletto.
I am elected.
wrong: Io sono venuto eletto.
correct: Io ero stato eletto.
I was elected.
wrong: Io ero venuto eletto.
The difference between a static passive and a dynamic passive can be crucial. If you are invited to a party and the cake is already eaten, you have a big problem. If they are eating it at the moment of your arrival, the situation is much better.
The cake is eaten. <=> La torta è mangiata.
The cake is being eaten. <=> La torta viene mangiata.