Here is a link to a list of close passages between the Sun and nearby stars calculated to have happened in the past few million years or to happen in the future few million years. All of them involve passing within 5 light years, and some involve passing much closer.
Three are calculated to pass less than one light year from the Sun.
Naturally those close passages will perturb the orbits of many Oort Cloud objects, and tend to free them from orbiting the Sun and put them orbits around the galactic center parallel to the Sun's orbit.
There is also the question of the Sun's Hill spear or Hill radius relative to the galactic center.
The Hill radius is the radius within which an object can have satellites with stable orbits.
I found this online Hill Sphere calculator and set it up to calculate the approximate radius of the Sun's Hill Sphere relative to the galactic center.
I chose one solar mass as the mass of the "planet", a semi-major axis of the orbit of 26,000 lightyears, an orbital eccentricity of 0.01, and tried out various masses for the amount of matter within the Sun's orbit around the center of the galaxy.
Using ten billion 10,000,000,000 solar masses as the mass of the "sun" in the calculation, I got a Hill radius of 7.837 light years.
trying a mass of 100,000,000,000 solar masses as the mass of the "sun" I got a Hill radius of 3.637 light years.
Trying a mass of 150,000,000,000 solar masses as the mass of the "sun" I got a Hill radius of 3.177 light years.
The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius.
Thus, if the mass within the Sun's orbit around the center of the galaxy is between ten billion (10,000,000,000) and one hundred fifty billion (150,000,000,000) times the mass of the Sun, the outer edge of the true region of stability for Oort cloud objects should be somewhere between 1.059 and 3.9185 lightyears from the Sun.
This agrees fairly well with the idea that the Oort cloud has a radius of about 2 light years.
But about all of the thousands of close encounters with other stars which the Sun must have experienced in its 4,600,000,000 years of orbiting the galaxy?
Assuming that a star with 0.1 the mass of the Sun passes at a distance of 1 light year from the Sun, at that moment the Hill Radius of the Sun will be 1.478 lightyears, and the outer edge of the true region of stability will be 0.4926 to 0.739 light years from the Sun.
According to the list of closest stellar approaches, HD 7977, which is now about 246 light years from the Sun, approached within about 1.478 lightyears about 2,760,000 years ago. HD 7977 is a G0V class star with a mass about 1.2 that of the Sun. At that time the Sun's Hill sphere would have been out to 0.308 light years and the outer edge of the true region of stability would have been at about 0.1026 to 0.154 light years.
So I guess that a lot of the objects in the outer parts of the Sun's Oort cloud would no longer be orbiting the Sun but orbiting the center of the galaxy in orbits roughly parallel to that of the Sun, due all the close encounters which the Sun had with other stars and with various massive nebulae and star clusters.