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.
The Statute of Limitations is a limit on how long a legal action can be taken. Once the requisite time passes the legal action (prosecution, lawsuit, whatever) is no longer allowed. The running of a statute of limitations is a complete defense to a crime in most circumstances. We have requirements for timeliness in most cases because it is considered unfair to prosecute some crimes after a very long period of time has passed because it reduces the ability of the defendant to defend themselves. However...
Civil forfeiture is legal remedy that the State seeks against "guilty" property. That is, if the property has been involved in a crime it can generally be seized by the State and used for the State's purposes thereafter. They can seize drugs, money, weapons, vehicles, real estate, really the list is limitless. You can find the list in Title 63 of the Oklahoma Statues at Section 2-503.
People go to jail. Our local jail, the one with which I happen to be most familiar, is the Oklahoma County Jail on Shartel here in Oklahoma City. It has a rated inmate capacity of 1200 but routinely houses 2500 inmates. It's just chock full of people, some dangerous, some stupid, some crazy, and some dangerously stupid and crazy. Combined with the overpopulation this is an extremely dangerous situation for both the inmates and their custodians, employees of the Sheriff.
Can the police search you, your car, or your premises? It depends.
One thing it depends on is if you consent. The US Supreme Court has instructed us that a consentual search is always legal. So lesson number one, if the police ask to search you, under no circumstances should you say yes.
Another thing it depends on is if they have probable cause to arrest you. If they do, then a search is allowed as being incident to arrest. Whatever they find can be used against you.