An offshore corporation cannot do business within the country in which they are incorporated; this allows the company to take full advantage of the low- to no-tax benefits that jurisdiction may offer.
There may or may not be residency requirements, employment of nationals necessary, or other considerations asked of the corporation by the offshore jurisdiction.
An offshore corporation can appoint a registered Agent who can act on the behalf of the corporation. The corporation is legally liable for all the transactions done by the registered agent. These agents play a role of a co-coordinator between the clients and the corporation.