Can a person open a new account with the same company once a charge off has been dropped from a credit report?

There are no laws (so to speak) preventing such a transaction. It is highly unlikely, that a company would accept a consumer who failed to honor past obligations. The person would be considered a "high risk" and not exactly a desirable customer. If the SOL for the resident state has not expired, the account is still collectable. Even though it may not be showing on the person's CR.