If a defensive midfielder is injured.....

[BeckStar]

Well Becks answer comes from experience and is an excellent answer.

I have a different answer, put this guy as mid sub and FORGET ABOUT IT!

You can't set auto sub for DMC tho, if your DMC get's injured he won't get substitution.. even if you've got a player like that

About you'r player, You could have only 3 sub players and cover all possible possitions(with 1% possesion penalty in some of cases.)
Formations with 3 defenders (DC DC DC)
AMC-MC-DMC(also covers DC and ST with 1% possesion penalty)
AML-ML-DML(also covers x AMR-MR-DMR WITH 1% possesion penalty)
GK

An easier sub tactics right here
If you've got a team playing 4-3N-2W-1 you could simply buy:
DC/DMC(also covers DR DL & MC)
ST(also covers AML AMR)
GK