The usual thing is an actor gets offered a role,
and signs on. The contract can often leave him at
the mercy of the production company - there are
plenty of stories of actors having scripts changed
on them, or films edited into something completely
different, without their ability to have any input.
Usually, unless they have lots of clout, they can't
have any influence on the disposition of the final
product - to prevent release of something is pretty
much impossible. They try to select a good project
based on a good script, and a good group of people
doing the production. Then they do their job, go
home, and hope for the best.

Then the production studio makes decisions about how
to distribute the result. They may decide the film
is unmarketable, and write it off - there are stories
of multimillion dollar embarrassments languishing in
film vaults - or they release with anything from no
promotion, direct to DVD, to major theatre placement.

The actor can only choose what to do based on paycheque,
or artistic interest, but preferably with an eye to
what it can do for their professional stature.
Sometimes signing on to a riskier production can
result in a great performance, and things work out
great; and sometimes what looks like a good idea
crashes and burns.