Does the Apple Watch work (specifically fall detection) with prepaid plans such as Boost Mobile?

Your watch uses the phones number to make calls,emergency or otherwise,for fall detection you will need an apple watch 4 or higher and a phone with ios14 or higher.

If you have an iphone 6 as your tag line says then you will need a new phone at least an iphone 6s.

You need to ask Boost Mobile if they support Watch number sharing with iPhone.

I guess not, but best you ask them.

Anyway, if you have an iPhone 6, it will not pair to a new Watch.

You need an iPhone model capable of installing iOS 14.7 before you can pair it with a new Watch.

Fall Detection, read here => Use fall detection with Apple Watch - Apple Support