How a stop becomes a case
Store staff can generally detain someone they reasonably suspect of shoplifting for a reasonable time and call the police. In New York, most shoplifting is charged as petit larceny, while higher-value or certain other takings can be charged as grand larceny. Leaving the store is not always required; concealing merchandise with intent to take it can be enough, so being stopped before the exit does not end the question. Self-checkout scanning errors have become a common source of accusations, and the store's own transaction logs and video can show what actually happened at the register. If anyone used force while trying to get away or keep the goods, the case can be charged as robbery instead.
The store's letter is a separate matter
New York and many other states let retailers seek a civil penalty from a person they stopped, and these demand letters are often sent whatever happens in criminal court. Paying the letter does not resolve the criminal case, and the criminal case is not resolved by anything you do about the letter. Whether and how to respond depends on the amount, the facts, and the state, so show the letter to a lawyer rather than paying or ignoring it on impulse. Do not contact the store directly about either matter.
The first days after a stop
Keep every paper you were given, including any ticket, property receipt, or written notice barring you from the store, and do not return to that location. Keep receipts, bank records, or app data that show purchases, especially if a scanning error is involved. Theft offenses can carry immigration consequences even when the amount is small, so anyone who is not a citizen should raise that with counsel before entering any plea. Students and people in licensed or security-sensitive jobs should also raise those concerns early, since a shoplifting record can show up in background checks.