"The policemen run into the bank."
Translation:A rendőrök befutnak a bankba.
According to previous (very helpful) comments the "be" before futnak implies that they actually end up in the bank right? Does that also mean that if the "be" is left out, so you get " A rendőrök futnak a bankba", that they don't actually end up in the bank? Or does it mean the policemen are in the process of running into the bank and it is still unsure whether they actually end up there?
Your second option is correct. They are in the process. But they are probably going to be inside at the end.
This is kind of how Hungarian deals with what English does with the various tenses. Simple, continuous, perfect. Hungarian only has the simple tense. So these little tricks are used for that purpose.