Has he been hospitalized recently?
Was he treated with invasive devices like respiratory support equipment or urinary catheters?
What is he complaining of?

Klebsiellae species can cause a variety of clinical syndromes.

He has colon cancer that has spread to the liver. It was diagnosed last year.
In April, he was hospitalized, had fever and felt nauseous - now he feels better (he's at home).
Doctors have tried 3 different antibiotics that they say to be the best, and still it didn't die.

K. oxytoca is one of the main member of this genus responsible for most human infections.
It's a opportunistic pathogen, meaning that usually do not cause disease in a healthy immune system, but, a compromised immune system (cancer sufferer), however, presents an "opportunity" for the pathogen to infect.
There are many multidrug-resistant strains of Klebsiella (antibiotics don't kill them), that are highly virulent (ability to cause disease), and have an extraordinary ability to spread.

Has this bacterium infected his lungs?
Does he experience thick, bloody sputum?

No, the bacterium is only in his liver, he had fluid analized last week and it was still there.
Well, I understand that he is not very strong, as he is ill...

I guess your father has cholangitis, a bacterial infection of the biliary tree, that is superimposed on an obstruction of the biliary tree due to a gallstone, cancer or stricture (narrowing). Infection can spread to hepatic ducts (liver ducts), causing serious infection.
In half of these cases, Klebsiella is the cause.
Poor health status is an important contributing factor.

Best wishes for you and your family!
Marija

Thanks again. He's going to the doctor this week, I'll post here any news about it.

You are welcome anytime!
Hope you father feels better!

Thanks,
My father has done blood tests again and got the confirmation that the bacteria is still there, but not on the blood, so it isn't spreading. Quite good news, in fact.