There are forces of gravity everywhere, even in the weightlessness of space, there's always gravity. Orbits, like the earth around the sun or the satellites we launch into orbit around the earth, or moon around the earth are a kind of balance between gravity and velocity.
Voyager 1 isn't in orbit, (It is around the Milky-way, but lets ignore that for now) it's flying out of the solar-system at 38,000 MPH so in essence, your question is about escape velocity from the Sun.
Voyager is currently about 131 Astronomical Units from the Sun.
At 131 Astronomical Units, the escape velocity from the sun is a bit under 10,000 MPH, so the answer to your question is no it won't stop, relative to the sun. It'll slow down, but it won't slow down any more than 28,000 MPH, at least until it gets close enough to another star to have a measurable impact on it's velocity.
If it meets a dual star system or star/planet combo (less likely), it would get a gravity assist either speeding up or slowing down. A star will also likely change it's direction, but, of-course, it will be long out of fuel by then.
If it was flying at a little bit under 10,000 MPH, it would eventually slow down close to 0 velocity relative to the sun, but it wouldn't ever actually "stop", it would either gradually escape or gradually begin to fall back - either into an orbit or back into the sun. (I can run the numbers with more accuracy if you like).