In the event that, except where: trong trường hợp, trừ trường hợp

Trong trường hợp (in the event that, in case of) sets a condition, the way rules and notices say "if": Trong trường hợp mất thẻ, khách hàng cần báo ngay cho ngân hàng. If you lose your card, notify the bank immediately. It's followed by a noun (trong trường hợp khẩn cấp, in an emergency) or a whole statement (trong trường hợp trời mưa, if it rains), and the rule comes after a comma. In laws, trường hợp alone often opens a sentence the same way, with thì before the rule.

Its partner trừ trường hợp (except where, unless) comes after the rule and names the exception: Không được đỗ xe trên vỉa hè, trừ trường hợp có giấy phép. No parking on the pavement, except with a permit. Regulations pair the two all the time.

Compare the everyday words. Nếu … thì is the plain "if". Lỡ is "in case something goes wrong": Đem dù theo, lỡ mưa. Take an umbrella in case it rains. In Hà Nội: Mang ô đi, nhỡ mưa. Trừ alone is the plain "except". Trong trường hợp is what these become in a contract, a law or an official notice.

Trong trường hợp is common in news and papers too: trong trường hợp xấu nhất (in the worst case). Trừ trường hợp is mainly legal. In conversation, nếu and lỡ are the natural choices.