Yes, without a fully defined scenario, there's no reason, value or meaning in saying something might "stop".
If you mean in terms of a nonrotating, pointlike, classical object, in pure vertical motion with no lateral velocity, following a Newtonian trajectory, without reference to a rotating or accelerating (other than gravity) frame, and no other outside forces (like wind resistance) -- and please take note of how many conditions one must apply to be rigorous here -- then one can say it "stops", as in velocity = 0, at one point during its path: the apex of the parabolic trajectory. This does not occur for a defined duration of time, but is an instantaneous event only. We use calculus to describe such conditions. If you prefer nonzero bounds, then we can define the limit as there being a duration of time dt such that the velocity is v +/- dv, for some dv and dt that exist. In the limit, we take both dt and dv to zero, but any will do.
Note also, there is nothing special about the point where velocity goes to zero. We can make just as remarkable a claim about the two points adjacent to zero, or where it's going 1 m/s, or 10, or whatever; any velocity that happens to appear during the trajectory. (Or including velocities that don't, if you allow extrapolating to earlier and later times while ignoring possible collision, or allowing that the number of points may be zero, one or two, or many, for any velocity we choose to ask about.)
Tim