Our Sun has a spherical bubble of planetary bodies, asteroids and debris localized at the outer point of the heliosphere, which is as far as the solar wind reaches before it dissipates. Contrary to what many believe, the objects of this region doesn't have their own trajectories. These objects are in fact stationary in this position, held in place by the outward pressure of the Solar wind. The corresponding force of nature, keeping them attracted towards the Sun are of course gravitation.
Our binary twin star, Nemesis, indeed has its own Oort Cloud, showing similar properties. Because Nemesis is not a planet (as in Planet X), nor is it a failed star due to lack of mass (suggesting a Red or Brown Dwarf). Nemesis is likely a Neutron star, more precisely an old Pulsar star. The visibility of Nemesis is very limited, since it mainly emits light in the infrared spectrum. It does however have some solar wind, consisting primarily of emitted protons and Alpha particles.
But since Nemesis has a very weak photo- and chromosphere, the solar wind will consequently not be very strong. And with a weaker solar wind, the closer to the star itself the Oort Cloud will be located. It is my estimation that the Oort Cloud of Nemesis arrives some 63 years before the star itself passes by the Earth. The total time span of cosmic upheavals will be close to a 130 year in length.
The passing of the Nemesis Oort Cloud through our Solar system is problematic in many aspects. The Oort Cloud represents a gravitational boundary, correcting the velocity of Earth, depending from what direction Nemesis arrives, compared to the ecliptic of our Sun. When Nemesis arrives from below the ecliptic, it pushes Earth to have a greater speed, thus shortening the year with 5 days. When Nemesis moves in from above the ecliptic, it instead reduces the speed of Earth, resetting the parameters to a "standard" 365 day year.
The gravitational shockwave will trigger a global Earthquake, which will be something out of the ordinary. The shaking will cause buildings to crash, roads and bridges to break. Great tsunamis will sweep in on coastal areas, doing great damage. The passing of the debris field will make burning meteors sweep the skies. Prior to that, gravel and Ice rain may affect crops and private properties. Occasional boulders and asteroids might even strike the Earth, causing problem if they hit sensitive areas.
Life will go on after the passing of the Oort Cloud, there will likely however be some problems with the electric grid and the infrastructure, for a while. The greater concern is when the Pole Shift takes place, but my estimation is it won't occur until sometime around 2068.