[DaveASA/FED]

The rule you are looking for is rule in NFHS is 10-3-3, and you are correct they have to stay in the same lineup position for the entire set under normal conditions. There are exceptional substitute situations for injured / ill players in 10-3-6 also listed below.

ART. 3 . . . A re-entering player shall not return to the set during the same dead ball in which the player was replaced. The re-entering player shall assume the original position in the serving order in relation to other teammates.

ART. 6 . . . When teams have exhausted their 18 team substitutions or when no legal substitutes are available, an exceptional substitution is permitted only for an injured/ill player in the following priority:

a. By a teammate who has never played in the set or a player who has played
in that position earlier in the set;

b. By any legal teammate on the bench, regardless of previous position played. An injured/ill player replaced by an exceptional substitution may not re-enter a set in which the exceptional substitution takes place. A team
may not play with fewer than six players if there is a legal substitute (including an exceptional substitution) available;

c. An exceptional substitution is counted as a team substitution if the team has not exhausted its 18 team substitutions.