Subs
 

Can a team send in a sub after a made basket? Or does a stoppage of play need to occur?

Ball must be dead and the clock must be stopped... No the answer to you question is no

NFHS rules

Stew in VA

Don't think stoppage of play .... but stoppage of CLOCK.

Depending on your rule set, even a stoppage of the clock doesn't provide a substitution opportunity. NCAA clock stops on a made basket with less than a minute to go, but unless there is a timeout, no subs.

I can't think of a NF situation that would inclued a clock stoppage without the chance to sub, but if there is one, I'm sure someone with provide it.

Just me trying to be precise.

No Substitutes
 

NFHS Rules: Before first of two free throws. Clock is stopped. Official still has the ball so the ball is dead. No substitutions allowed, unless injury, blood, or disqualifiction is involved, until after the first free throw is completed. There may be other examples, but this one came to mind first.