{{xpos, ypos}} = {x, y} /. NDSolve[{
x'[t] == y[t],
y'[t] == -1.5 (x[t]^2 - 1) y[t] - x[t],
x[0] == 0.5,
y[0] == 0
}, {x, y}, {t, 0, 100}];
{{xpos, ypos}} = {x, y} /. NDSolve[{
x'[t] == y[t],
y'[t] == -1.5 (x[t]^2 - 1) y[t] - x[t],
x[0] == xpos[100],
y[0] == ypos[100],
WhenEvent[
Norm[{x[t], y[t]} - {xpos[100], ypos[100]}] < 0.1,
"StopIntegration"
]
}, {x, y}, {t, 0, 100}]
(* The above integration stopped at 7.06; example visualization: *)