We can't say that. You're missing the other forces in the picture. If a body is subjected to a constant net
force of F newton for t seconds, its change in momentum will be, magnitude of F multiplied by t, yes. Here the 50 N isn't the net force.
Force isn't a substance to be transferred. It is applied.
And regarding the situation you mentioned where the string breaks, if the string had indeed maintained a constant force of 50 N for the time 0.5 s on the body under the influence of no other
forces before breaking, then yes. the body should have a change in momentum of 25 Kgm/s.