In BC Small Claims court, you can sue defendants who reside outside of British Columbia. Rule 18 of the Small Claims Rules include a few sections that deal with suing people who reside outside the Province:
Service of a notice of claim outside British Columbia
(6)A notice of claim may be served on a person outside British Columbia if
(a) the person is
(i) an individual who normally resides in British Columbia, or
(ii) a corporation that has assets in British Columbia but is incorporated outside British Columbia and is not an extraprovincial company,
(b) the transaction or event that resulted in the claim took place in British Columbia, or
(c) the registrar gives permission (see Rule 16 (3)).
How to serve a corporation outside British Columbia
(6.1)A notice of claim authorized under subrule (6) to be served on a corporation outside British Columbia must be served
(a) by mailing a copy of it by registered mail to a place of business or registered office of the corporation outside British Columbia, or
(b) by leaving a copy of it
(i) at a place of business or registered office of the corporation outside British Columbia with a receptionist or a person who appears to manage or control the corporation's business, or
(ii) with a director, officer, liquidator, trustee in bankruptcy or receiver manager of the corporation.
So, someone can start a claim against someone who lives outside of British Columbia assuming that the nature of the dispute involves British Columbia. There are a few rules that determine whether a dispute is one in which a court in British Columbia can decide - for example, British Columbia will not assert jurisdiction over a case in which two motorists, one from Alberta, one from Saskatchewan, get into car accident in the United States, with a car rented from Ontario. But, the BC courts may assert jurisdiction over a case in which a BC resident receives goods in British Columbia under a supply contract signed in British Columbia, even if the shipper of the goods resides in Ontario.
If you decide to sue a foreign defendant in British Columbia, then you will need to take the extra step of registering the judgment (assuming you receive one) in the foreign province. So, if you get a judgment in British Columbia against a company in Ontario, then you will need to take the extra time and spend the money to register the judgment in Ontario. After that, you will need to follow Ontario rules and procedure to enforce the judgment and collect on it.
Alternatively, you can avoid this extra cost and fee by starting your lawsuit in the foreign jurisdiction. You would then need to consider the cost of traveling to the foreign jurisdiction when required.