The speed of the probe doesn't change with regard to the assisting body. It is direction that is changed.
If a hyperbolic orbit about the sun comes in with a Vinfinity of 5 km/s, it will exit with a Vinfinity of 5 km/s.
Unless it happens to swing by a planet. From the planet's point of view incoming and outgoing speed are also the same. Again, it's direction that is changed. But a direction change with regard to a planet could be a speed change with regard to the sun. Thus a fly by of one of the gas giants might slow a hyperbolic about the sun to an elliptical capture orbit about the sun.
Here is an illustration of how a lunar swing by might change an hyperbolic asteroid's path to a capture about the earth:
At the moon's neighborhood, earth escape velocity is around 1.5 km/s. Thus dropping the asteroid's speed from 1.98 wrt earth to 1.14 wrt earth brings the rock into an elliptical capture orbit about the earth.
In a similar fashion, a swing by of one of the gas giants might trap an object from outside our solar system into an elliptical capture orbit about the sun.