The figure you are referring to is the under 10k rule. This applies when you make a bank deposit or you purchase anything over ten thousand dollars in cash the bank or the place of purchase are then required to report that to the IRS.
No, it is not illegal to have that amount of money on you, but unless you can prove that you acquired that money from a legitimate means you can lose that money to the government. I handled many of these cases when I was a prosecutor. It is called asset forfeiture. It normally occurs during a routine traffic stop. If police discover a large amount of cash (with or without the presence of drugs) they can and often do seize the cash. This becomes a problem for you because while under our constitution a person accused of a crime is never required to prove that they are not guilty , it is always the burden of the state to prove the guilt of an accused beyond a reasonable doubt, this is not true in asset forfeiture cases.
If the police seize your money, the district attorney then gives you a notice of seizure. If you fail to respond to that within ten days you can and often do lose the money. If you respond timely then another series of legal petitions and answers are required and most people fail to file the appropriate paperwork to get the money back timely. Only a lawyer well versed in asset forfeiture alw can really help you. It is a catch 22 because in order to get the money back you have to first admit you are the owner, this often implicates people in a crime if they cannot show that it was derived from legal means.
The burden becomes yours (which appears unconstitutional) to request a hearing and to then show that the money is yours form legal sources. The police often seize money even cars even without the presence of drugs under this theory. If drugs are present and money is not the police argue that the drugs have not been exchanged for money yet. If the large amount of money is present but drugs are not the police then argue that the money is the product of an illegal transaction (the prior sale of drugs). Unless you can show through bank statements, casino winnings, or pay stubs that the money you are carrying is yours from a legal source I highly recommend you not carry large amounts of cash on your person or in your car, and do not keep large amounts of cash in your home.