Sometimes during the course of an arrest a person tries to get rid of contraband (usually drugs, sometimes guns, not usually anything else) so that when they are caught they don't have it on them. This is called a "throw down". There are a couple of issues that arise from this.
One, it can be a little harder for the prosecution to place the contraband with the defendant. After all, once caught, the defendant didn't actually have possession of the contraband and the prosecution must reconstruct the action, after the fact, to prove the defendant at some point actually had it. This will depend heavily on what the police officer is willing to report that he saw. If he clearly saw the "throwdown" and records it in his report, then the reconstruction is not usually terribly difficult if the arrest occurred nearby. If the pursuit goes a good distance however, then it may be harder to prove possession, or possibly to even find the contraband in the first place.
Two, when a defendant throws down contraband they are actively relinquishing control of it (abandoning it). This means that there is no requirement for a warrant to search and seize the contraband. If the police (or any witness really) sees the abandonment, then it may be possible to connect the defendant to the contraband.
This is all very fact specific. One time we had a guy throwdown a trafficking amount of meth under his own car after he was stopped. It was easy for the prosecution to connect him to the meth. We got him probation anyway, instead of the ten years imprisonment that the DA wanted, but not because of the throwdown.
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