Answer
Browse Abandonment text messages can only be sent to individuals who have compliantly opted into your store's SMS program. Learn more about growing your subscriber list here. This is required for all abandonment automations (e.g. Abandoned Cart, Browse Abandonment, Product Added to Cart, etc.).
Once the subscriber has explicitly and compliantly agreed to receive your brand's marketing SMS messages, browse abandonment automation messages will begin sending after a cookied subscriber browses your shop.