I heard about drug cut off levels. does it mean that a person can take a drug like diazepam and still test negative for a drug test if the drug level in the person's body is not high enough to be detected regardless of the time he took the drug?

This depends on the sensitivity of that test. Some can detect trace amounts of a banned substance, some tests would only detect it at a higher level. Drugs vary in their "half life" or the time it takes for 1/2 to be eliminated through metabolism. Some have a half life of a few hours or less, I can think of one with a half life of 22 days. It can take 4+ half lives to fall to undetectable.