When it comes time to renew their lease, I'd try to get rid of them.

For most owners the goal is to keep tenants, not get rid of them. 

The seller may be selling because they have bad tenants they can't get rid of.

I've had to get rid 3 people for non-payment this year but in my area rooming houses are run like a hotel so we can just tell them to leave and/or call the police if they don't want to go nicely.

If there's even a hint of a problem, get rid of the cat, tenant, or both.I allow cats, but they must meet my requirements.

They didn't want to deal with any showings and just got rid of it because it was inherited.

Don't get duped by warranties or guarantees or anything, just get rid of them.

I'm considering purchasing the house to bring up the neighborhood, my own property value and just get rid of the eyesore.  

I will be rid of them in 5 months - but yes you are all right that I should have evicted them way sooner. 

Get rid of all units that don’t fit that mold.