The rule that covers all cases is that you let subs come in before a FT only if the ball will remain live on a missed FT. So (as was said above) that's before the first shot of a 1-1, before the last shot of multiple FT attempts for a common personal foul (there can be 1-3 attempts), or after the last FT attempt for an intentional, flagrant, or any technical foul.
The exception above for a DQ'd player would also apply for an injured player that needs to be replaced immediately.
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