Yes and no. Many antibiotics do as you say, that is they only suppress the bacterial growth but do not kill the microbes. These antibiotics are called bacteriostatic. Streptomycin, however, is bactericidal antibiotic as far as I know, and thus it kills bacteria that it affects (it is bacteriostatic on lower concentrations, though). There are many bactericidal antibiotics, you should look at some pharmacology guide for more details.

And if somebody wonders now why do we use antibiotics that do not kill bacteria, the answer in a nutshell is this: the human immune system can get rid of vast majority of even severe bacterial infections as long as the bacteria are not dividing constantly. Bacteriostatic antibiotics stop the spreading of the infection, and immune cells have time to destroy the remaining bacteria.

just to elaborate on what biohazard has said and put it more in layman’s terms, there are two types of antibiotics: those that only stop the bacteria from dividing and those that actually kill the bacteria. Let’s analyze them individually:
Antibiotics that kill bacteria (like streptomycin, kanamycin, rifampin etc) will kill any bacteria that are not resistant to the antibiotic if the bacteria are in the presence of the antibiotic long enough. Most of these antibiotic work by inhibiting protein synthesis in bacterial cells, so any cell will ultimately die unless they are resistant to the antibiotic.
Now the antibiotics that stop bacteria from dividing (ampicillin, penicillin etc) work like this: if the bacteria divide, then they will die. But if the bacteria just sit there (it is called a persister state) without dividing then they will be quite fine, even if they are not resistant to the antibiotic. The reason for this is that these antibiotic mostly affect the synthesis of the cell wall. if the bacteria divide the daughter cells need to make new cell walls, and if they cannot (because the presence of one of these antibiotics) then water rushes in the cell by osmosis, the cell swells and bursts. So it is not true that these antibiotics only stop the bacteria from spreading and wait for the immune system to clean up the stuff. Even though the immune system definitely does have a role in this, it has long been known that if you treat a patient with ampicillin for an infection, it is possible that some persister cells will start multiplying after the treatment and trigger a secondary infection.

Cheers,
Andrei

it is by far most common for them to be in the culture media, but they can enter cells. I am guessing the effectiveness of the antibiotic would then depend on whether the antibiotic can get inside the cultured cells. If it can and the bacterial cells are sensitive to it, then i guess they would get killed. Of course, if the bacterial cells are sensitive to the antibiotic then they shouldn’t be able to make their way inside your cultured cells in the first place.

Cheers,
Andrei

Do you have a problem with tissue cultures contaminated with microbes?