I'm a Vietnamese citizen traveling to Taiwan with a valid US visa. Can I enter Taiwan visa-free if the US visa will expire during my stay?

According to the National Immigration Agency of Taiwan:

(Applicable to citizens of India, Indonesia, Vietnam, the Philippines and Thailand)

Citizens of the five listed Asian countries should initiate an eligibility check before filing an online application for Travel Authorization Certificate:

Basic requirements (All conditions must be met):

• The applicant's passport is valid for at least six months. (This means that the passport is valid for at least six months when its holder arrives in Taiwan and not when the application is filed online.)
• The applicant should possess a return plane or ferry ticket.
• The applicant is never employed as a blue-collar worker in Taiwan.

Additional Requirements: (Possessed one of the following documents).

• The applicant should possess a valid (1) Permanent Resident Card or
• (2) Entry Visa

Of any one of the following countries: the United States, Canada, the United Kingdom, Japan, Australia, and New Zealand; or one of the signatories of the Schengen Agreement. (including an electric one).

A single-entry visa becomes invalid once it has already been used. However, a used single-entry visa might be acceptable for the purpose of immigration inspection to enter Taiwan, if it meets the following conditions:

• On the same continuing journey, the visa holder uses it to enter the visa issuing country prior to his/her arrival in Taiwan; and

• The visa holder will arrive in Taiwan before its expiration date.

The applicant must present the required documents for inspection when entering Taiwan; entry will be denied if the required documents are not produced.

Therefore the answer is yes, you can enter Taiwan at any time while your US visa is still valid, even if it will expire during your stay. Don't forget to file the online application for a Travel Authorization Certificate before you arrive.