Asteroids are not typically that large, of course there's exceptions. But the gravity on this supposed intersolar object would be almost definitely miniscule. Finding a very large asteroid passing through the solar system seems to be rare, as far as I am aware, though I admit my knowledge here is very limited

So why would anybody want to live on such an asteroid? It's not going anywhere fast. The nearest star intersection is likely to see will be somewhere in millions of years in the future. So all these people are going to go live on this asteroid which is basically living in outer space with no gravity, which will have all kinds of problems for your body, and now they're cut off from the earth and have to live in a small self-sustained society which is by its very nature going to have extraordinarily strict rules and limit people's personal freedom to be huge degree, limit what you can do what you can see if you can talk to, definitely limit who you can sleep with and how much population you're allowed to grow.

Also that in a few million years maybe it will pass through some of the solar system that may or may not have some useful thing to visit?

Nah. That's not a mission that's going to happen even if it were feasible