If an injury had happaened in Pakistan in a franchise or out let of a U.S. company, could we file a lawsuit in the U.S. because the negligence of the specific franchise is due to the negligence of the U.S. company.
Your question is hopelessly unclear. Is the injury a personal injury, an economic injury? Is it to the company, an employee, a customer? What statute of limitations are you referring to? You really need to give considerably more detail, or meet with an attorney who can help you identify the issues.
As Michael mentioned, it is not clear from your question which statute of limitation applies. Limitations depend on the type of claim you want to pursue, i.e. negligence, slander, contract dispute. It does not depend on where the suit will be filed.
